The good news is, that you are riding in a place that WILL make you faster over time than someone that sticks only to the flat areas. I'll bet that you are a lot faster than you think on flatter terrain.
To get faster where you live, I would do 2 things:
Go on 1-2 longer rides per week, always going about 10% - 20% further each week, as time allows. Spending longer in the saddle trains more of the slow-twitch muscles and overall aerobic conditioning. Go your normal speed on these longer rides.
On all of your other rides, I would attack the hills, using different pedaling strategies to max-out your exertion for the targeted muscle groups. You want to have burning rubbery legs, and be breathing so hard that you almost see stars when you get to the top of each hill. Sit and grind at a low cadence up some, sit and put it in the easiest gear you have and spin as fast as you can on others (making sure to practice spinning FAST down the next hill, to get used to the fast leg-motion - shoot for 120+ rpm downhill), stand and slog HARD up some hills, stand and move your feet faster on others. You can mix it up on the same hill, sometimes, if you like.
The point is to not kill one set of muscles on your legs, while really blasting your aerobic system, and to give you lots of different ways to attack hills. Over time, you will figure out which combination of climbing approaches works best for your body, and you will naturally gravitate towards that when you really want to push it faster up a hill.
Oh, and have fun! That is the point, yes?