Travel agents will be able to arrange a vacation package that will include tickets, but often people prefer to make their own arrangements for travel, hotels and theater tickets themselves. Doing this allows you to tailor the vacation to your exact requirements as well as cutting out the middle man. It may save a few dollars, but this is not always the case.
You may find it difficult to secure tickets for a particular show because, in many cases, travel companies have block booked thousands of seats to the most popular shows to allow them to offer appealing packages to their customers.
Tickets for some plays and shows are booked out and the only chance of obtaining a ticket is from someone who is willing to sell one. The Internet makes this sort of arrangement much easier than in the days of ticket touts, though the touts still exist.
You can look in the classified ads of the evening papers of the city where you are planning to stay, these may be available online, though there may be a subscription fee to pay. Alternatively you can try the auction sites where tickets for even the most popular shows are always available - at a price.
There are specialist ticket-selling agencies where you can book a ticket for any show or play, in any city in the world, for the face value PLUS a booking fee. These are not black market outlets and they often only have tickets for a few hours for top shows and artists. You really need to be organised well in advance to queue or access their websites if you want a ticket for a top artist or theatre.