There are no 2 bedroom apts that rent for only $1650 in PB, OB, or anywhere else close to the beach. Most 2 bedroom homes are $2,400 per month at the low end at the beach. Most properties do not allow smoking and the new laws will be coming into effect in 2 years in most states banning all smoking in residential zones. Also, most places do not allow pets. Get your pet certified as an E.S.A. as a service animal. That will allow you to rent with your kitty.
Also, I would look at 1 bedrooms for that budget. If you can quit smoking, that would save you a ton of money ! It's just not accepted in CA and you will feel a bit ostracized. Just keeping it real. You can also share a 2 bedroom / 2 bathroom with someone for about $1,200 ; but again the kitty and smoking will eliminate most possibilities. Perhaps try looking out in east county or down in imperial beach areas. Try the Clairemont area in San Diego because it is very central and within 5 miles of the beach. That is your best bet. Craigslist, Trulia, Zillow, or Hotpads (sharing) are the best places to look. Good luck to you !