If you have a recreation card, you can reserve courts at UCSD by calling 534-3486 and giving them your rec card number. There are lots of courts, many with lights. The north courts are the newest, but the Muir courts south of the math building are also very convenient. There are also courts as part of the Warren campus. There are probably over 20 courts on campus. UCSD Recreation also offers many courses to learn how to play tennis. These courses are pretty inexpensive and you will find others of your ability to play with.
Another possibility is to play doubles with the Tennis Exchange. This is a group of adults who are matched up to play evenings and weekends at various courts in town. It costs a membership fee (probably around $100 a year) and also a dollar per set, no ad scoring. What I like about this is that you do not need to have a partner and you can play on the spur of the moment. They also have trips to fun places around San Diego and Palm Springs where they play tennis for an entire weekend.
For the more competitive, you might try the Tennis League. For $30 a 3 month season, they provide you with an email and phone list of players who you set up matches with. You determine your level of playing ability based on US Tennis Association rankings. Every time you play a match, the winner records the score on the website. If you win 5 matches, you get to play in the playoffs, which is a single elimination tournament. It’s fun, it is a great way to meet other people at your level, and it gives you an opportunity to work on your game.
The La Jolla Tennis Club has 9 nice courts and is in downtown La Jolla (5 minutes from campus). They have one of the oldest tournaments in the country. Some of the older players have played in the French Open. You can probably pick up a game there if you come in the afternoon around 2:00 pm.
Finally, the Balboa Tennis Club in Balboa Park has over 1400 members. There are a lot of courts, tournaments, etc. to be found there.