I went to college at UCSD so I'm fairly familiar with the area but I've also been on a college budget most of the time so I'll leave it to others to recommend more sophisticated things.
If you like scenic or ocean views, I'd definitely check out Mount Soledad in La Jolla and the Cabrillo Monument in Point Loma. The views are beautiful at both places.. and the lighthouse is really pretty too.
I've always had an apt here so I can't comment on the service of the hotel but the hotel is in a really great location. There are so many good eats in Gaslamp, you could just look up reviews on
www.yelp.com for whatever you're craving. I really like Fish Market on N. Harbor Drive, it has a great view too and it's inexpensive. Extraordinary Desserts is far and away my favorite (the location on Union and not the 5th ave location).. they have the BEST fudge and you must order at least one chocolate cake
I also like Caffe Italia on India St for gelato.. Little Italy in general is worth at least one meal. There are lots of little dessert places around La Jolla so if you walk up from the Cove, I'm sure you can find something. I've always tried to go to the Cove during low tide so I could see the tidepools and I've never timed it well.. but there isn't really a bad time to go to the Cove unless it's really windy. Be prepared to spend time looking for parking since it'll probably be busy. The cove is scenic, relaxing and everytime I go there, there is some couple taking their wedding pictures
Downtown La Jolla is a nice shopping area though in my college immaturity, I was more impressed by the houses and cars.
SD has great beaches but my favorite is Coronado and you can take the ferry from the Broadway Pier to Coronado in 15 minutes. The ferry is two miles away from the beach so you can take bus 904 or maybe some others too.. the Hotel del Coronado is pretty famous and right on the beach! They have better sand than the other beaches.. too bad about alcohol being banned from beaches now :/ If you can't make it out to Coronado, Pacific Beach, Ocean Beach, and La Jolla Shores (in spite of all the college kids) are great neighborhoods too. Balboa Park is nice looking.. the museums themselves have always been underwhelming to me. If you like Mexican food or burritos at all, you must try it here. If you haven't been to the Wild Animal Park or Zoo before, WAP is more intimate but the new panda cub was born at the zoo a couple weeks ago! Hope this helps!