I agree with the post above regarding nature. I didn't go to Galapagos, but I'm told it's amazing. Quito is actually quite central. From there, you can reach most of the tourist locations, and trip time isn't very long.
I was working in Ecuador, and I didn't do a lot of traveling myself. However, some coworkers of mine traveled every weekend. They'd head out on Friday for the beaches, Yasuni, the hot springs in Papallacta, Mindo, etc, etc. We were there for 12 weeks, and they took a trip almost every weekend.
Safety is a big issue. The downtown area of Quito, La Mariscal, is filled with military police carrying large guns at night. I was working for a government organization, so I often heard many horror stories of things happening to tourists. The Ecuadorian newspapers run columns every day about "inseguridad." There are TV programs that allow viewers to call in and report crimes because the police are viewed as corrupt/ineffective.
People complain about crime in Buenos Aires... Ha, it has nothing on Quito. And I was told by some of my bosses in Quito that it didn't even compare to Central America.
I avoided taking taxis off the street; 90 percent of the time I called. Be careful when taking money out of ATMs -- one of my coworkers had her card data swiped somehow at an ATM. Watch your account online! And if you're a U.S. citizen, register with the U.S. Embassy in Quito (via travel.state.gov).
Remember Quito is really high up there. For the first several weeks, my body fought the altitude. If Quito will be your first destination, take it easy. The teleferico (cable car) there is amazing, but I wouldn't take it the first couple of days that you're there. I went up on the third day, and the shocking height that you climb combined with the lack of oxygen almost made me pass out! But the view is so, so, so beautiful.
Have a great trip!