I lived/rented in Santa Barbara for 5 years so here's my two cents. The rental market is super competitive in SB/Goleta due to the University and the incredibly high house prices. Therefore, landlords tend to be very, how shall I say it, anal, rude, picky, etc.

So, be prepared for some of that. However, the last year that I lived there I had a great landlord that let us have a dog and didn't request an additional deposit. All the rentals listed in the paper you can find on
santabarabranewspress.com.
The only other advice I can give you is stay away from Milpas and Nopal St. area. There will be a lot of house rentals around there and they will be cheaper but it's because it's a higher crime area. I really like the Santa Barbara Foothills/Mission Canyon area (around Foothill Rd.). But other good areas are San Roque, the Mesa (near the city college), and the east areas of Goleta.
Hope this helps. Good luck with your move!