Georgetown is NOT just M Street or a few blocks of Wisconsin. If you walk the streets a few blocks to the north e.g P street) that parallel M street, you'll see some wonderful examples of colonial era townhomes. That, IMHO, is the beauty of the place. The chains along M street you can find anywhere. Blocks of beautifully restored housing you can't.

For dining you are unfortunately limited to M street and Wisconsin.

Capitol Hill/Eastern Market? Great choice to explore and get a flavor of the city. Try to see LOC and the Folger. both free and interesting. Good dining south of EM.