Simonp and I have had our tandem for a year now so I can share what I've found so far.
The good bits are :Staying together on the road (Simon usually rides fixed so he is faster uphill but slower downhill than me on solos so riding together is a PITA in the hilly terrain around Bristol).
More social, you can generally always hear each other to chat rather than needing to pull alongside.
Navigation in our case made easier by having twin Garmins on the bike. I actually have mine really so it gives me data to look at on the back, but I can also keep an eye on where the next turn is etc. Some stokers keep map/ route sheet on pilots back.
Your stoker can pass you food, swap water bottles over for you and give you a back massage.
Stokers can't see the road ahead so well, but we can look at scenery and over hedges and walls plus chat to other riders more easily than on a solo bike.
The tricky bits are:Sorting out starting and stopping, particularly if you are both clipless which if you plan to ride 100k+ I think would be a good idea. It is very much easier for the stoker to remain clipped in for short stops and rotate the pedals around for you to your preferred starting position being careful not to whack you on the shins with any pedals in the process. If you are heavier and stronger than your stoker it should be fairly easy for you to hold the bike up like this with her clipped in but requires her to have total faith in you. You need an emergency 'bail' command for if you need her to unclip and out a foot down e.g. when you suddenly need to stop on a very steep climb or your chain snaps or something. I can imagine there is much more room for error with this kind of coordination if your wife is a much less experienced cyclist than you.
Cadence preferences. I am a bit of a grinder whereas Simon more of a spinner so I sometimes find his cadence a bit tiring. I've tried to increase my natural cadence to be a better match and he tries to use a silty higher gear for my sake. It would be way easier if you both had similar cadences anyway.
Arse comfort. On a solo bike I can take the weight off pressure points like my arse by putting more power through the pedals, or freewheeling for a bit. On the tandem I am at the mercy of the pilot who might not be wanting to freewheel so much (my pilot tends to forget he has a freewheel at all sometimes!) or has the cadence so high I find I can't 'catch up' with e pedal stroke enough to take my weight through my feet so much. Add this to often a more upright riding position as a stoker and it is a recipe for more arse soreness. And then there are the bumps in the road the stoker can't see coming so can't 'brace' or get out of the saddle for unless the pilot calls it in plenty of time. We have a suspension seat post on the rear, but even with that I've needed to use a wider heavier Brooks saddle than on my solo bikes to get comfy. I did PBP on a solo in '11 without getting a significantly sore arse, but my first Audax on the tandem (the Gospel Pass 150k) I was begging Simon to freewheel while we were going uphill
It did get better with more tandem riding and we subsequently did an SR, including the BCM 600 and a 1000 mile tandem tour round France without me having significant problems. I can imagine a relatively new rider might have more issues than someone like me with a leather arse from doing lots of miles previously though. If you try it and she has problems like that make sure she knows it will get better in time with gradually increasing mileages and the right saddle.
I never had any trouble with my knees before riding a tandem. However the longer audaxers caused an issue that I'm still not 100% recovered from. I'm not the first stoker to find I have knee issues, so watch out for this. Changing my saddle fore-aft position wrt my pedals has helped. A pro bike fit could be your friend here, we probably should have got one or at least checked where my knee was with a plumb line before riding off into the distance!
Group riding can be a little bit tricky initially. By this I mean with groups not that skilled at group riding, such as can happen on CTC rides and large mass start Audaxes. Riders often overtake you uphill only to totally getting your way on the downhill that follows. Or worse they can force you to stop suddenly uphill or in the wrong gear which can make you want to strangle them. You may find yourself wanting to ferociously guard your hard-won momentum!
One other negative has been transporting it around. We ended up getting the expensive gas-lift rack for the roof of the car. We prefer to ride to the start of events or get trains, but it can be tricky to get it on some types of train. We managed to do an Easter arrow and get the train back from York to Somerset but we had to go via London not Birmingham and getting it reserved on the train was not that straightforward. Simon spoke to some guy from the train operator on the phone who asked him what a tandem was
We did make it home eventually though. On our trip to France we opted for the simpler option of just riding there (100 miles to Portsmouth, ferry to St Malo, then 200 miles to Niort for the Sem Fed). If you only want to do local events on your tandem then it won't bother you much, but otherwise buying racks and things is something to consider. The first rack I tried needed 4 people to lift the bike onto it
If you and your wife like each other and want to spend as much time as possible together, then I would say go for it! Hope to see you on the road (we live in Axbridge and are often on Bristol area rides, we have a silver Orbit)