A week in each place should be enough - in fact, that's pretty ideal. It's those 2-3 day whilrlwind jaunts into each city that I feel are shortchanging travelers. A week is fantastic, as a matter of fact.
Naturally, the longer a trip is, the better and more in-depth it'll be, as long as you can afford it. So if you can, I don't see any reason NOT to go longer, and I don't think anyone here would disagree. We're all a bit biased and addicted to travel, though
As for the money - my typical burn rate in Europe would average to around 50€/day, not including transport between cities/countries, so for a month I'd be looking at 1500€. Sounds like it'll work!