Limited budget

Depends on which cities you visit! Germany and Austria are very inexpensive countries, and food and accommodation are cheap compared to many other Western EU countries. I think you can do 2 weeks with that amount.

For about a week - maybe? That is unrealistic low. First, just pull the airfare out. Depending on time of year it could be 12, 1300. So that leaves about $2500. Depending on what you do and where you sleep and how far your travel, that could easily hit $300/day so your have about 8 days. There are so many variables that could effect the answer that it is nearly impossible to provide a decent answer.

Hi Teri, for how long, a week, two?
I could manage a week,but not much longer if that has to include airfares from where I live, and if you don't mind a budget style trip. I would choose one base to explore from , not do alot of travelling about ( just daytripping of course) .. but there are others who prefer a different travel style and likely have their ways of making it work. Since I am not sure what your airfares are its hard to figure what you have left to live on ,, so perhaps you could price out a few airfares and see what you realistically will have left to deal with.. to live and tour .

You can easily travel on $2500 (excluding flights) for two weeks if you were careful. That's $150 per day. We seldom spend that much when traveling. The only thing is that you might need to limit the # of places you visit, and possibly pick less expensive locations. That might keep you out of Venice, Paris & London. A big money saver is food. We eat a big (free) breakfast, snack mid afternoon and only pay for one meal per day. And we don't eat in expensive restaurants. We just love to visit their grocery stores to get picnic items. The other trick is to stay in budget accommodations, and the internet makes finding them so easy. Last April, we spent 70 euros tops for our trip to Italy. If you're youthful, a hostel wouldn't be desirable. Flying open jaw'd is also a money saver, and avoid London for connections due to high grounds fees and taxes. Fly into a central location where you want to visit and out of another city at the end of your trip. I'm seeing some $1050-1100 flights to some places for May, but prices skyrocket for mid-Summer. We have no problem traveling in the frugal manner, rather than in the continental style.

Provided you can get your air for under $1000 pp, I think your are comfortable for 10 days on the ground, maybe 12 if you spend carefully.

I'm with David. It can be done. Take advantage of free breakfast, if it's included. Stock up on bread/cheese/charcuterie/yogurts/fresh fruit & veg at markets or supermarkets. Not drinking alcohol, while boring if you like an adult beverage from time to time, saves a LOT of money. We just got back from a week in London and spent $900 on our hotel, $2400 on airfare, and about $100 a day on food/drink/spending money. We had a great time - in a very spendy city - for well under $5 large. Go for it!

research research research research
research do extensive research. figure out a list of EVERYTHING you want to do in these areas and look up the exact cost. then do a food budget. after that, see how much you have left for hotels, use booking.com (or whatever) to see if you have enough for hotels. hotel costs can be adjusted down if you are are not picky. if you have no qualms about staying in dorm style hostels, you should be golden.

Possible? Yes, depending on how long you want to stay and what your standards are. Why not price this trip out yourself and see if it is doable. You need: 1) Price of airfare for two. 2) Price of accommodation. Be sure to check hotels and hostels. If you check hostels, be aware that prices are generally per person. 3) A realistic food budget. $30 per person per day is a bare minimum. 4) Local transportation costs. You need to plan for every movement where you are not walking (and remember that public transit can take care of a lot of it on the cheap). 5) Sightseeing costs. 6) A budget for gifts.
7) Add all that up and add 10-15% for emergencies.