There are SO many free or nearly free activities to do in San Diego.
Balboa Park is a great place to stroll through (including the rose gardens across the street). The often have free concerts. In the summer they do free movies on the lawn. The museums rotate one day a month when admission is free each month. Check the online calendar for all the activities happening in Balboa Park each month.
Hike Torrey Pines. Beautiful views, very romantic. You don’t have to hike up the big hill to the top if you don’t want to. You can park at the top of the hill and hike around the easy trails at the top while taking in a view of the ocean. (Parking is $10 if you park inside the park. If you want to save the money park outside and walk in).
Ride bikes around Mission Bay.
Stroll around La Jolla cove, see the seals at the children’s pool, check out the caves, or best of all snorkel in La Jolla cove (you can buy a snorkel set at Walmart for $7).
Stroll through farmers markets or street fairs. Hillcrest and Little Italy both have great farmers markets with live music. Enjoy the free samples of food. There are numerous neighborhood street fairs in North Park, Hillcrest, South Park, etc. throughout the year. Look online for local event calendars to see what’s going on.
Hike around Mission Trails, Cowles Mountain or Iron Mountain.
Liberty Station in Point Loma often has big events with free entertainment, music, etc. They probably have an event calendar online somewhere.
Visit Cabrillo National Monument. I think it’s $5 per vehicle. The views are incredible and the tide pools at the bottom of the hill are fun to explore.
During times of year like when the Festival of Sails or other similar events are happening it can be fun to just walk around down by the harbor, or Shelter Island, take in the views, maybe stop somewhere for one drink or a coffee together, etc.
Have a bonfire/picnic at the beach, or near Mission Bay. Watch the free Sea World fireworks.
Buy a $5 block of ice from the grocery store and ride ice blocks down the hill at Presidio Park. Ok, maybe this one is not a good idea for an early date, but it's seriously so fun. You can really fly down the hill. It's like sledding but you don't need any snow on the ground.
In general, there are lots of beautiful views and places to walk around and explore while you talk and get to know each other. In the beginning, on early dates, food and drink can be kept to a minimum. Stop for one drink, or a coffee, or share a dessert together at some point while you’re walking around or doing some activity. There’s really no need to go out to fancy restaurants and have a sit down dinner until after you’ve been on a couple dates with the person and you know you want to spend more time with each other. The first couple dates are best kept shorter and more causal anyway, with activities to give you something to do while you talk and provide a distraction if the conversation wanes.
Check out the San Diego Reader calendar for all sorts of activities going on around the city each week. The Union Tribune and City Beat probably have event calendars online too. Many activities listed in those types of calendars are free or cheap. Check out Groupon or Living Social for discounts on activities like kayaking or stand-up paddle boards, and discounts on admission to museums or Scripps Aquarium.