Just to make sure I understand correctly, do you mean you actually have a preference for going to college outside of California? Or are equally fine either way depending on the other factors involved? Either is a fine attitude but it may help us to know which reflects your current thinking.
In terms of urban schools with interesting CS options, I agree CMU is a possibility. Very much a fit school but it is right in the heart of Pittsburgh, and also right next to Pitt, where you can actually take some classes if you like. Obviously you would need to check their NPC.
And you could consider Pitt itself, including because it is a larger college, but also sometimes it is less expensive including because it has OOS merit. I note it is easy to arrange to visit both Pitt and CMU if you are interested, and Case is not far. Speaking of which . . . .
In my circles, Case Western is often described as the CMU of Cleveland in terms of there being a somewhat similar academic mix. It has a great location and also merit.
WashU is not necessarily the first school people think of for CS, but it has been investing a lot in the area and has some interesting initiatives that lean into its strengths for multidisciplinary studies. It has a very good location in St Louis. Not much merit, though, so check the NPC.
Minnesota is a great suggestion for an urban school with strong CS that would probably make your budget.
Finally, Boston University has an interesting CS program, including an integrated BA/MS if you might be interested in something like that, and it is a significantly larger than usual private. Like all the notable Boston schools it gets a lot of applications these days and is not necessarily the most generous with aid, but you might look into it just because it seems like a good fit to me.