These are expensive cities. With some research, you might be able to find some small double rooms for around $200 per night in unique, potentially charming small (boutique) hotels without full service--no restaurant (continental breakfast only, but probably not worth the cost if it's priced separately), no or very limited room service, no parking, no fancy cable TV, no pool or health club, etc. Figure out what you really need and will use during your stay. For instance, if you're not traveling in summer, AC isn't an issue, and in these places, you would want to explore local restaurants rather than eating in the hotel. How important is location to you?

Will you be reserving a sleeping compartment on the night train? This can be shockingly expensive, roughly the price of a normal room in a top hotel, for a small space with rather basic bathroom facilities at best.