Recently, I had the amazing opportunity to spend 6 months in Paris. I used the opportunity to travel on a shoestring budget across the continent, and visited a bunch of places. My advice to anyone who is in a similar position would be to definitely make the most of the travel opportunity, see the continent for all that it is.
Here are some wonderful trips you can make. Some can be done even over the weekend, if you are an active traveller.
Belgium- I visited Brussels, Antwerp and Bruges, all over one 3 day weekend. Brussels is a great city, with amazing nightlife, no matter what people say, and you can see the whole city in a day. Dont miss bruges. Its a half day trip from Brussels, and again, you can walk along the entire city. Antwerp was a nice, quiet kind of town, but you can give it a miss.
Spain and Portugal- Club these two amazing countries together for an amaaazing trip. I spent 10 days in both countries together, and it was sheer bliss. The beaches in both these places are breathtaking, and if you are a beach bum, these countries are for you. The southern algrave region of Portugal is a gem. Do not miss it at any cost.
Italy over a weekend (YES)- It seems impossible, but i spent a day in rome, and saw a LOT of it. Obviously, if you are the kind of traveller who likes taking their time, and soaking up the culture, take atleast 4 days in rome. But if you want to get a feel of the city,a nd are not big on long lines and endless museum tours, give that a miss and just walk around the eternal city. What's more, is that I also got to take a train ride to florence and spend a day and a half there, eating every ice cream i could lay my hands on.
Amsterdam- 2 full days here. You will not get bored of this city. so much to see, and so many things to try :P Just land up, and a friendly coffee shop owner will tell you what to do, over his finest stuff.
11 days in eastern/central Europe- closer to summer, do give Budapest, Prague and Vienna a visit. Vienna is much like other western european cities, with grand buildings and the Euro, but Budapest and Prague are like a breath of fresh air. The strakly different architecture, behaviour, and most of all the PRICES strike you first thing when you land up. The cities are flooded with young people, and you'll never run out of things to do. Special mention to Prague and it's nightlife. Spend a good 3 days here, walk around, and definitely go for their world famous city pub crawl. You wont remember a thing, and have the best time of your life.
Hope this helps all you travellers.
Cheers!