My partner and I purchased a tandem this winter and have since done a good bit of riding on it. A few thoughts:
1. You'll want to purchase a road tandem bike, as others have mentioned. This will cost a minimum of $2k unless you can find a good deal and/or a used tandem. We purchased a 2008 Cannondale Road Tandem 3, which had a MSRP of $1799. You can put aerobars on it if you wish, but I would shelve that idea until your stoker is okay with it (see points (3) and (5) below).
2. They say that a tandem will not change your relationship with your partner significantly--you'll just get wherever you were going faster. e.g. If you have a poor relationship, you'll find that you willl argue and bicker a lot, but if you have a great relationship a tandem will cement that. In my experience, I've found this to be true--my partner and I have a great relationship and we always have a good time on the tandem.
3. Riding a tandem is really all about the stoker. You need to keep your stoker happy, safe, confident and comfortable. This means making sure that
(a) the bike you buy fits the stoker,
(b) your stoker has a comfy saddle and bars,
(c) your stoker feels safe on your rides, and
(d) your stoker can stop when s/he needs to.
4. Take it *very* slow on your first few rides. There is a learning curve that took us about 100 miles of riding over 8 or 9 rides to figure out. This includes things like mastering the correct starting technique, deciding on a comfortable distance from the kerb/yellow line, figuring how to ride in traffic, choosing a cadence, standing to climb, turning, and more. What we did was we actually *drove* the bike out to a deserted, flat state forest for our first few rides. We were able to practice starting, stopping and riding in a straight line without having to worry about cars, hills or other distractions.
5.
Riding a tandem is really all about the stoker. The saying goes that "the stoker makes no mistakes." That doesn't mean that you make all of the mistakes (feel free to blame weather, the terrain, etc) but the stoker makes none. How can she make any mistakes--she's not in control of the bike!
If the stoker wants to stop, you stop. If the stoker wants to slow down, you slow down. ESPECIALLY at first. Essentially, you are selling your stoker on the cycling experience, and since YOU are the one controlling her cycling experience, you jeopardize her trust in you on future rides if you don't listen to what she wants and needs during the ride.
To close, I would like to post a picture of me and my partner with our tandem during one of our first rides on it this winter: