Hi Cloudy,
Since you're going during winter and you'd probably prefer somewhere with milder weather, and also as cost is an issue, I'd suggest South of France, Spain, and perhaps Portugal. These places are cheaper than most of Western Europe; in particular, Switzerland and Northern Italy is very expensive. Southern Italy may also be cheaper, but it's harder to get there.
So you may wish to concentrate on South of France (Cote D'Azur, Provence, Languedoc, Basque, etc.), Spain, and Portugal. All relatively untouristy places, beautiful scenery, and since you're going during low season (as long as it's not Christmas / New Year), it should be cheaper as well.
When exactly are you going? December, January, or February?
Another very important thing to consider is what is your main mode of transport? The best way to see the countryside is to rent a car and drive around; trains are a poor second choice, they are only generally good for inter-city travel. With a rental car, you can save costs by not staying inside the city proper where hotels are more expensive, but stay at the outskirts in some charming B&B where not only is it cheaper, but the friendly hosts can give you suggestions on what to do and a whole lot of other useful recommendations!
To go into the city, you can choose to drive (city driving is a little more challenging than driving in the countryside) and generally incur expensive parking charges, or you can drive to some train station or bus stop and get into the city via cheaper public transport.
There are lots of ways to save money and Europe need not be as expensive as people think, as long as you choose your destinations carefully and do lots of planning!
See for example our trip for four persons in France in 2005; under SGD 3k per person for 19 days.
http://rtan.net/France/
One possible suggested itinerary is: Fly to Paris, take the TGV (high speed trains) down to Avignon. Explore Avignon for a few days, then grab your rental car, and head towards Spain, generally hugging the coast. Stop somewhere in between for the night, then head towards Barcelona. Stay a few nights. Then continue on, and basically you keep hugging the coast going in a clockwise direction until you get to Portugal, and continue right through to the North coast of Spain, then through the South West corner of France, then you cut through to Toulouse and back to Avignon, then take the TGV back to Paris, spend a few days there, do your shopping, and return to SG.
By keeping to the coastal areas you get very mild weather. If this sounds like the sort if itinerary you'd like to do, we can discuss further from here. You'd need minimum 3 weeks (4 weeks is better) for this itinerary, but it will be the holiday of your lifetime as you will experience many different cultures and foods, and you will see much in terms of scenery and nature!
Oh yes, F&E is a lot of work, but it's well worth it, as you can see from our great pictures. And we can help you through the process!
