When looking at possibilities for living in the east side of San Jose, Costa Rica there are Barrio Otoya, Barrio Aranjuez, Barrio Escalante, and Los Yoses. These are all in San Jose just outside of downtown. Barrio Escalante is a trendy neighborhood with many restaurants and bars. Going a little further east you have San Pedro home of the University of Costa Rica. Also in this area is Zapote and Curridabat. These are all good possibilities to consider.
When looking at the east side of San Jose a good option for a hotel is Hotel Aranjuez, the have 2 bedroom 2 bathroom apartments at a very reasonable price per month, includes electric, water, cable TV, and internet..