The rental market in LA is a bit slow right now with a lot of places not selling being leased. The current rents on the MLS listed are at 2826 for the entire building per month which is under market. I have seen 1 bedrooms lease for around 800-1000 in the area. If the units are updated and the building is put into better condition I would say 1400-1500 would be reasonable. Given it's proximity.
If you have any other questions, please let me know. In order to bring the rents up to market you would have to evict with just cause which I could connect you with an attorney or discuss with you further your options.
Keller Williams Wilshire
Without seeing the inside of the units and the condition I would guess $1,050-1,300 per month per unit. I sell a lot of property in Hollywood and Hancock Park and have several investment property listings that will be coming on the market soon. Let me know if you are looking for anything in particular or have any questions.
Keller Williams Realty