Lee,
I would recommend getting tickets via the internet ahead of time if you want to be sure to see a certain show. The good ones usually are filled up and unless you go see the shows that have been out for a while, you will not get great seats, which really make or break a show in my opinion.
Wicked was very enjoyable, Jersey Boys is a very hot show and may be very hard to get tickets unless you get them in advance. Also, that show has good music - from the 50's/60's era of American Teen Idol, Frankie Valli which if you are not familar with the era may not mean much to you. Three are a number of good plays that have been out for a while that won't break the bank, and will appeal to you regardless of the story line.
I found that in London, for example some of the cultural differences were hard to discern in some of the plays we saw. We actually left early because there were some scenes all relating to local culture that made the play where we did not understand the story line.