Depends on what you're looking for....there are many good options. My running experience is mostly limited to the western US, so take this for what it's worth. In order (for this time of year, September-October)
1. Central coast of CA. This is the best weather of the the year on the central coast. From Santa Barbara to San Francisco, you can find cool runs, cool hotels and eateries, and beautiful beaches
2. Colorado / Northern Utah. Probably shouldn't lump these together because they are in 2 different states, but you've got interesting cities surrounded by majestic mountains with tons of running opportunities. It's just starting to get cold there, and you might get some unexpected snow, but the fall colors can be spectacular (Never been to the northeast in the fall, I'm sure that has more spectacular fall colors). Special recommendation for Logan, UT. I went to grad school there. Check out the Crimson trail and the Narrows trail in Logan Canyon. I was in Denver this summer and the variety of both running options and urban amenities was great.
3. Southern Utah / Northern AZ. During the summer, it's pretty dang hot there, but there is a wide variety of terrain to run. Although there is a lot of desert, it can be beautiful. AND, there are some pretty beautiful forested areas as well. Get some 9000' elevation running in on the Kaibab Plateau outside of the Grand Canyon north rim before it gets snowed in.
I'm not super familiar with the PNW or the upper Rockies, but I'm sure there's some great running up there as well.
I'd be interested to hear about cool places to runcation on the east coast, as we're probably going to be doing some traveling there next year.