This will be a fun thread!
Here's part of my list. I do a mix of trail running and regular stuff.
San Diego: you've got a ton of options from beach to the (awesome) Bayfront path that takes you past the airport, to Balboa Park. Balboa Park has a bunch of trails in it and really you wouldn't know you were in a major city once you get deeper in to the park. Just ran five miles through the park last week.
Portland: Downtown has a plethora of runs along the river. I haven't run in Forest Park myself, but have friends who do 10, 20 or 50(!) miles up there in a day. They're crazy but claim to love it.
Boise: awesome paths around the river downtown and by Boise State. Some flood in the spring, which can make things challenging. Easy to get to from the airport. Great city too.
Minneapolis: downtown is great and you can easily hit five or six miles along the Mississippi. There's some off road stuff in Prospect Park around St Paul and the U but I haven't run them myself.
Dallas: There's lots of trail running around downtown Dallas. The Katy Trail is my favorite, but my coworker who lives there loves Cedar Ridge and Lake Lewis.
San Jose: the Guadalupe River trail is easily accessible from downtown San Jose. It goes on for quite some distance, but it's also inhabited by several homeless camps. They usually keep to themselves, but just be aware.
Tucson: my favorite spot for true trail running. You can go for miles and see nothing but critters. BE CAREFUL: if you're not familiar with the desert or the town, DO NOT go deep in the desert or you will get lost. Bring water, a phone with offline maps and watch for snakes. If you want desert running on a paved and trafficked path, Sabino Canyon is great. It's a seven mile round trip that gains about 500 feet from start to finish. There's also a long path along the usually dry "river" in town. Not particularly scenic compared to desert, but it's a great spot. Park at the Trader Joe's on Campbell & River and hit the path.
Phoenix: You can easily do 10+ miles along the canals, which are accessible from many of the airport hotels on 44th Street. Some canal trails are paved and some are a hard pack gravel/sand material. Don't run in July unless you're crazy or up at 4a.
Maui: Just run along the beach. I usually get a good mix of beach and road running when I'm there.