When shopping for airfares, choose the "Multi-city" (or "Open-jaw") option. I did some exploring myself back in September, and it seemed to me that to keep the cost down, I needed to stick with two cities served by the same airline alliance. If I selected one city served by the United group and another served by the American group, I got not-budget-friendly fares. (It looked as if I might be paying for two one-way tickets.) So you may need to explore a bit.
From my origin, I sometimes see good deals into Milan, Rome and Munich, but it really does depend on where you're flying from, and when. You can start by looking at roundtrip fares to get an idea of what might be your lowest-cost gateway cities and perhaps less expensive weeks or days for travel. Some of your possible gateways will probably get eliminated at that step.
The subject of finding a hotel upon arrival in a city has come up several times recently, and the consensus appears to be that it's not generally a good idea. I'm one of several posters who traveled that way in the (distant) past, but now that we have the internet and easy access to Wi-Fi, it's simple to use a hotel-booking website (I use booking.com but don't claim that it's better than other options) 1 to 3 days ahead of time. Then your arrival in the city is stress-free. Several things besides the internet have come into play since the 1980s: cheapo intra-European airfares have a lot more Europeans on the move, and the economy in places like China has improved to the point that there's a middle class able to travel far and wide. Demand is up greatly, and the travelers competing with you for hotel rooms will mostly not have waited till the last minute to reserve something. You will generally get the least-desirable/more-costly places, or you may be frozen out completely.
Even booking a few days ahead is not without some risk. You need to have done your research so you're confident you're not going to bump into some sort of big-deal special event that could suck up all the hotel rooms weeks or months in advance.
These factors add to the risk:
- Low budget for lodging.
- Insistence on a "special" sort of place--charming, with a view, with a balcony, with a good breakfast, etc. Within each price range, that sort of place gets snapped up early.
- Need for air conditioning (not all places north of the Alps are air conditioned, and you're traveling during a potentially very hot period). Several times I've been forced into a higher hotel category than I wanted because all the lower-rated places with a/c were booked up.
- Insistence on staying in a particular town, especially in a central location in that town, rather than just nearby. Again, you may have to compromise on proximity to sights or the train station to avoid moving up one hotel category.
- Preference for longer stays in one place. At the last minute, it can be easier to find a place for just a night or two than for 3+ nights.
Still, the flexibility of last-minute hotel bookings is worth it to me. I booked most of my rooms just 24 to 48 hours ahead of time during a 4-1/2 month summer 2015 trip and a 3-month summer 2016 trip. I did arrange a 10-night reservation in Barcelona a month or so ahead of time because of the length of the stay and the comparatively high cost of hotels in that city. And I think it's smart to make a reservation as soon as you're sure when you want to arrive in a city; there are no bonus points for dilly-dallying unnecessarily.
You probably won't benefit from having a car, but we'd need a list of planned cities to give a well-thought-out answer.
Ditto the railpass. It's unlikely one will pay off, but to be sure one must compare the cost of point-to-point tickets with the cost of a pass. I think the countries you plan to visit have generally reasonable rail fares. Germany, in particular, has some good deals
