Answer: Santa Cruz
, Avila Beach and Santa Barbara
would be your best bets. Santa Barbara has the warmest water, but Avila Beach has slightly warmer air temperatures, at least during the spring. In the summer months the differences are minimal in these 3 places, with temperatures averaging from 72 to 78 degrees.
The water temperatures on the Central Coast are by no means warm. They average between 53-55 degrees (F) in the spring. However, in Santa Barbara they average around 57-59 degrees. Water temperatures peak in late August and September, averaging 60 degrees in Santa Cruz and Avila Beach and 65 in Santa Barbara. So if you've got your heart set on swimming, Santa Barbara is your best bet.
All of these places have south facing beaches, which is one of the factors that makes them a bit warmer.
Santa Cruz and Santa Barbara are large enough cities that you should be able to find some good budget lodging. Avila Beach is a small town, but it does have some modestly priced accommodations. If that fails, you can try nearby Pismo Beach.
Hope this helps you find the perfect place to relax.