Closest beach will probably be in coronado. That should be about a ten minute ride on the freeway and over the bridge.

Best of Both Worlds...

Hi!
Welcome to SD!
The Gaslamp is very close to shopping [Horton Plaza in particular] & the water [the marina].
However, if you're looking to be near the beach & exclusive boutique-style shopping, then you might want to consider Downtown La Jolla. There are a lot of exclusive boutiques [just like Rodeo Drive, but not as snooty] and the beach [Windansea, the site of a lot of photo shoots, like for the Sports Illustrated Swimsuit issue, as well as the La Jolla Shores, which is very nice beachfront].  
Folks might suggest PB [Pacific Beach], but that's way too touristy, crowded and the shopping there is kind'a weak.
I hope that this helps you out.

Pacific or Mission Beach not far at all from Downtown!

Reasonable rates this time of year with rooms right on the beach & very close to Downtown SD!  Enjoy your visit.

Gaslamp is a must....

But don't go to Coronado unless you want to see the hotel Del.  Go to La Jolla Cove,  Cab ride could be pricey but the hotel maybe able to help you out. And, there may be a welling gentleman who could help you out...