Here are some suggestions:
Point Loma area:
Cabrillo National Monument: not a lot to see there but spectacular views of the city and the ocean. Tide pools area is fun.
Fort Rosecrans National Cemetery: same views as Cabrillo, and it's free. Yeah, it's a cemetery, but this has to be the most spectacular setting of any cemetery. My grandparents are buried there.
Sunset Cliffs: a long stretch of coastline with nice ocean views, great place to watch the sunset
Ocean Beach: The "hippie" neighborhood with great culture. Also the longest pier on the west coast. The best fish tacos in the U.S. are at the South Beach Bar and Grille, the last bar on Newport before the pier. Really high-quality and during the happy hour (I think 3 to 5 pm but I'm not sure) the prices are lowered. Two people can stuff themselves and be out for $20 total. Enjoy the atmosphere of the neighborhood and take a stroll along the pier.
Beyond Point Loma area:
Mission Bay Park: Huge park, my favorite spot is the Vacation Isle, the island that contains the Princess Resort, off Ingraham street, the southern half of the island is public parkland and has nice relaxing beaches and views of the boats going by.
Mission Beach: zoolike atmosphere but fun. You can ride a bike or rollerskate up and down the very long concrete boardwalk and people-watch. There is a very old roller coaster which has been restored and would be fun at night.
San Diego Bay: Spanish Landing park another good place to watch the boats go by. Along Harbor Drive are boat tours that you can get on and go around the bay. Also the Star of India is there, the oldest sailing ship still afloat in the world. You can take a tour of it for a small fee. There is also a ferry to Coronado.
Coronado: Not a lot to see but a nice view of downtown San Diego, and of course the famous Hotel del Coronado, very old and very expensive, but they have a small museum downstairs and you can look at pictures of "Some Like it Hot" being filmed there.
Downtown San Diego has very little of interest, except lots of restaurants and bars in the Gaslamp Quarter area. Seaport Village is just a shopping center next to the bay. Petco Park is just an expensive ballpark. Horton Plaza is just a shopping mall.
Old Town San Diego is north of downtown, and has tons of Mexican restaurants, the best is Old Town Mexican Cafe. There is also a state park which is historic, shows how that part of town looked 100 years ago. Presidio Park, up the hill next to Old Town, is a lovely park and a good picnic spot. Nice views there too. There is a small museum at the Presidio which is the orignial location of Mission San Diego. The current Mission San Diego de Alcalá is several miles to the east, in Mission Valley. I take my Mom to mass there every Sunday. It is a large, very old church with some nice courtyards and a small museum.
Little Italy, north of downtown, is small but naturally has great Italian food. My friend Luigi is one of the owners of Assenti's Pasta, on India street, knockout fresh pasta that you can buy and take home. Or eat there in one of the many restaurants, the owner of Mona Lisa lives across the street from me. Not much else to do there except eat.
La Jolla is a ritzy community, still part of the city of San Diego, north of Mission Beach and Pacific Beach. La Jolla Cove is a gorgeous spot where you can go swimming. The Children's Pool has been in the news for about 20 years now, seals sit on the sand and there is a long, ongoing battle whether to remove them. The seals there have become an attraction themselves. South of there are more pretty beaches. Windansea Beach, on Neptune Place is a classic southern California beach, very attractive and there are usually a lot of surfers. The square building next to the street is the pump house made famous in "The Pump House Gang" by Tom Wolfe. La Jolla Natural Park, off Encelia Drive, has a great view of the coast but little else. Mt. Soledad, at the top of the hill, has terrific views of the city if the weather is clear.
Balboa Park, northeast of downtown San Diego, has so many things to see and do that it would take too long to type them all in here. Most of the main attractions are in the center or western section, including several museums, which charge to get in but sometimes there are free days. The botanical building is free though and has exotic plants. The rose garden is also free. That building appeared briefly in "Citizen Kane." The Spreckles Organ Pavilion has free organ concerts on Sunday afternoons at 2 and in the summer on Monday evenings in the summer at 8 pm. with world-ranked organists. Also free concerts of different types on Tuesday, Wednesday, Thursday in the evenings at 6 p.m. There are many other things to see and do at Balboa Park, and "Prado" is a quality restaurant there though not cheap.
San Diego Zoo is of course a paid attraction in Balboa Park, but well worth it in my opinion. Even the landscaping is worth it. They are gradually remodeling it from a cage/enclosure type zoo to a series of environments/ecosystems. Brand new this year is Elephant Odyssey. Take the bus tour if you want or just walk around. Giant Pandas, koalas, big cats, great Children's Zoo too. Walk through the lush Fern Canyon which most people miss.
Old Town Trolley Tours is a great way to get around town to the most famous attractions that tourists want to see, without worrying about driving or parking. You can get on and off where you want. I have not actually taken it myself but a friend of mine did and he liked it a lot.
http://www.trolleytours.com/san-diego/ Further away from the center of San Diego are other places worth going to if you have the time. Del Mar has nice beaches and the Del Mar Fair in June, held at the racetrack, and of course the horse races there in August and September. Encinitas, further north, has Quail Botanical Gardens, Carlsbad has Legoland for the kids, Tijuana to the south has shopping, tequila, Kahlua, vanilla, music and drug cartel violence. Rosarito Beach, further south on the Mexican coast, has the same, Puerto Nuevo, further south, has lobster, Ensenada, even further south, is a very nice Mexican city, far superior to Tijuana in my opinion.
There are mountains to the east of San Diego, which would make for a nice drive if you are interested. Take interstate 8 east, all the way to the Sunrise Highway, about 1 hour east of Point Loma. This is a beautiful road that winds through mountain forests, one of the last remaining forests in the county not destroyed by fire. There is a spectacular view of the desert 6,000 feet below, from a lookout that you get to by turning right off Sunrise Highway, the turn is not marked but it's right after the Desert View picnic area. Drive to the top and get out and if it's clear you can see the Salton Sea and even Arizona. Keep going north on Sunrise Highway and you will eventually arrive in Julian, about 2 hours after you left Point Loma. Eat lunch and/or apple pie there, the best apple pie there is at Apple Alley Bakery on the east side of the street. Come back to San Diego a different way, starting out going south on the same road you came in on, past Lake Cuyamaca, a beautiful spot, then going through Cuyamaca Rancho State Park, which was devastated by the Cedar Fire but is slowly recovering, then eventually meeting up with Interstate 8 again which you would take going west to get back to San Diego. A wonderful drive overall that will take about 3 hours plus any time spent at stops. If you like gambling, stop at the Viejas Indian Reservation, right on Interstate 8 at Willow Road, there is a free outdoor show every night at 9 p.m.