First of all, welcome to our city! I know you will love it.
As a San Diego Native, let me just say--get a car if you can. There are many beaches, and as someone said, if you want to do more sightseeing than bus/trolley riding, a car is your best bet--and I say this as a booster of bus/light rail travel. From where you are--and it sounds like you're more in Hotel Circle than you are in Old Town, getting to the Green line trolley is funky. It's not that it can't be done, but it takes time. Also, if you want to go to the beaches closer to your hotel, rather than North County beaches, you could park your car at the Old Town station and take buses from there, but you'd still have your car--from where you will be, you will be close to funky Ocean Beach, young Mission and Pacific Beaches, and a short car ride from the Embarcadero and Coronado. From what I can glean from your post, you are farther away from the Old Town station than you might think...
Just for ease of use, I do hope you get a car. But if you do decide to take pub trans, see if your hotel has bus schedules; no matter where you go, you'll be starting your journey on the bus. If there's a bus close by that will get you to either Fashion Valley or to Old Town you'll be in a much better position.
In any case, have a great trip!