It depends on what you are looking for. Are you looking for a cond? Co-op? or home? It also depends on your price point. The DC metro area has a pretty good bus system, so Glover Park or Burleith (which are not on a metro line) are connected to other areas via the bus. Other areas near Georgetown, to the Northeast you have Dupont to the east you have Foggy Bottom/West End. Both Dupont and Foggy Bottom/West End have metro stations.
Please let me know if you have any more questions or if I can be of any assitance.
There are many great areas that are close to Georgetown with access to transportation so it's really just a matter of personal preference and affordability. Generally, the closer to Georgetown, the more expensive but that's not entirely the case. Some of my favorite areas are Dupont, West End, Foggy Bottom, and Kalorama if you want to stay in DC within walking distance of Georgetown and be close to a Metro station. I live and work in this part of the city and would be glad to send you some great listings in these and other areas of the city if you contact me at firstname.lastname@example.org or 202-494-0714. I would welcome the opportunity to help you in any way I can.
All the very best,