I can’t say anything about the “where to go” bit, but packing I know.
Firstly, the idea that you can pack for three weeks is a myth. Unless you want to have a miserable time anytime you’re in transport, you do not want to try and bring three weeks worth of clothing.
The most clothes it is ever reasonable to pack is clothes for a week. So pack for a week. Yes, this means you will have to get your clothes laundered. But believe me, asking the hotel to launder your clothes (or even stopping by a coin laundry with your luggage) is way and many times more joyfull than trying to pull around multiple bags.
If you don’t have suitcases and whatnot, then good. Those big honking suitcase that roll around on four wheels and come up past your knee when set down lengthwise have no purpose in the world and exist solely because people who aren’t regular travellers think they need that much room.
What you want are the suitcases that come up to your lower thigh when set on end, are about as wide as your shoulders, and have an upsidedown-U shaped handle that raises up so you can pull it on two wheels. One for each of you. Then you want one all-purpose duffel-bag type thing for taking on the plane with you. You stick books, maybe a sweater for each of you, iPods, a pen, your tickets, and overflow into this bag. Your wife then gets her own carry-on size thing (you don’t get one.) When you are in airports or whatever, you put your carry-on size things on top of your suitcases and roll them around with the rest of the stuff, so you want to try and get it so they can be connected to the handle, or they’ll fall off.
You will want:
7 pairs of socks
7 pairs of underwear
6 t-shirts
1 nice shirt
1 tie
1 suitcoat
Depending on weather, and whether there’s a pool:
3 pairs of pants (including your suit pants)
1 pair of swimtrunks (if there’s a pool)
1 sweater
or
2 pairs of pants (including your suit pants)
3 pairs of shorts (including swimtrunks)
Shampoo, toothpaste, etc. (Assuming you are allowed to take liquids and gels on the plane)
Toothbrush, razor, etc.
If you have shampoo and toothpaste and whatnot, you want to put those in some sort of plastic bag. Oversized sandwhich bags are perfect, but a grocery store plastic bag and a rubberband will work just fine.