See 4 cities instead of 1
While traveling Europe I tend to follow this guide line however it's never really set in stone: 1 big city, then 1 small city and keep going in that rotation if possible. This allows me to get overwhelmed by the big city and then take in the sights and sounds of simple small town Europe (a vacation in a vacation?)
I like traveling to Europe before and after the summer. This allows me to avoid the crowds and long lines while venturing off solo or in a group. Exploring outside of tourist season also allows you to meet up with more locals who are on their holiday.
Take a moment while planning out the cities to see and find out which ones make sense in which order. This might seem like common sense but I've found people back track in their travels which kills a lot of time sitting on a train instead of exploring.
Only 3 days in a city? That's all?
Spending a week in a city might allow you to see the entire city inside and out but it also might prevent you from exploring other areas of any given country. I feel spending too much time in one area is putting all your eggs in one basket. And what if it's a basket you find out isn't that great?
Day 1 Generally I arrive in a city by mid day by train. Walk to the hostel and secure my bag and then hit the city running. Take in as much of the city as I can for one day because everyone at the hostel is most likely doing the same thing. Scope out where the local bodega is and any restaurants you might want to try.
Day 2 Start early, breakfast at the hostel and out the door. This will be the big sight seeing day to knock any major lark marks or museums. Lunch might be a picnic in a park from local market goods scoped out the day earlier. Dinner will be modest hit up any bars that evening with locals or people from the hostel.
Day 3 Last full day. This is where we'll finish up anything we didn't catch the day earlier, wander around and chill out. Dinner will be at a sit down restaurant usually recommended by locals and drinks later on in the evening. This is the chill out day, no pressure, no rushing around. The next morning will be early, hopping on the train to the next destination to get there by noon.
This approach allows you to sample a lot of cities and you'll have options to come back for more days on a future trip. I've been to Munich 4 times and I still can't get enough but I wouldn't want to stay there on holiday for longer than 4 days at a time.
3 countries, 6 cities, 16 days, all for under $2500. That's including plane ticket, food, and drink expenses. It's not difficult and you're not having to sacrifice much of anything. Just budget out your day with some leeway and go all out every 3rd day. This allows you to taste the local foods and still get that "I'm on vacation" cheat day.
A typical breakdown would look something like this: Plane Ticket $1000, Hostels $300, Train Tickets $400, Food & Drink $300. Crunch the numbers yourself and find out what you'd typically spend per day. Breakfast is almost always free due to hostels providing that for you. Lunch ranges from €5-15 and dinner would be under €20.
You'll get the best deals on exchange rates with using your ATM cards at one of the many cash machines conveniently places throughout the cities. Check if your bank reimburses your withdraws before you leave for your trip. That way you can take out smaller amounts instead of walking around with a lot of cash. It's also good practice to let your bank know your itinerary before you depart so your first few transactions over seas won't flag their system to potential card theft.
Exchange rates are better at ATMs
Food and Drink - Eating and drinking can sometimes run up half the cost of the trip. Grab the free breakfast at the hostel, then while out sight seeing, locate a local grocery or farmers market. Purchase all the picnic essentials then take it to a local park or ruined castle. Drinking at the hostels is almost always cheaper than at the bars by a large margin. You'll find the other savvy travelers do this as well. I found myself starting the night at the hostel's bar then heading out as a group to a pub to socialize with the locals. As stated above I tend to splurge on restaurants every 3rd day. Of course this is only when you're trying to be frugal. The alternative is to eat at restaurants the whole time which is extremely easy since there's a cafe or restaurant on every street corner.
Picnic at a ruined castle in Bacharach
Fresh fruits & vegetables at the Viktualienmarkt
Winter in Europe
It sounds crazy but traveling to a colder climate can actually be more enjoyable. I was lucky enough to experience Sweden during the peak of their Christmas season and absolutely loved it. The Swedes really know how to get into the spirit of the season. Pack for a lot of snow and bring proper snow boots. Wear all of your heavy clothes on the flight so you won't sacrifice vital bag space.
Days are short up north where the sun sets around 3pm. This makes for a hectic morning when you realize day light is a precious resource so you get all of your daily shopping done by noon. This makes the evens and nights seem to go on forever.
The silver lining is when every side street or open field is worthy of a post card. Snow falling on a tall brick cathedral in Uppsala reminded me of a living snow globe. Just remember, bundle up!