It is generally not considered that odd to travel for a major sporting event or even a concert, though I got a few strange looks when I told people I was traveling down to L.A. primarily so that I could see the Kronos Quartet. One generally does not travel all that far for classical music, instead going to support one's local chamber music ensembles and/or symphony (and perhaps hoping that a very good orchestra will be on tour and come through town).
While I don't keep precise track of their movements, I do occasionally check to see if Kronos Quartet will be playing nearby (not in 2016 unfortunately) or the Pacifica Quartet. Now Pacifica rarely or perhaps has never played Toronto, though they are coming to London (Jan 29 and April 8) and Hamilton (April 10). I think I'll be able to make the April 10 show, so I'll put it in my calendar of long-term events.
As far as Broadway goes, I've certainly combined museum and theatre trips, though I don't know that I would say I ever went to New York solely for a play. Now I did try to go to Brooklyn for The Iceman Cometh, but that went horribly, horribly wrong, so I don't think I will do that again. But I did go to San Francisco and Berkeley and Montreal to see Stoppard productions (Arcadia and the Coast of Utopia and Travesties, respectively), and I went to Ottawa to see an Arthur Miller play. And I am leaning towards going to Peterborough* to see Les Belles Soeurs, so I definitely do travel to see a show, particularly if it isn't produced often.
I am much less likely to travel strictly for an art exhibit, but it depends on the circumstances. I always try to bundle trips to cities with a visit to the art museum. Our upcoming trip to Chicago is based somewhat on the fact that the Greek exhibit, which we kept missing, is going to be at the Field Museum. I am fairly seriously considering going to Cleveland in December to catch a show about the Impressionists and their gardens. Probably the biggest trip I even scheduled around art was to see the Max Beckmann exhibit at MoMA Queens, but I was able to make it coincide with a work trip, so it cost me almost nothing. Ah, those were the days...
I have just booked travel to New York and Boston around the Toronto school board's spring break, and we will just miss an interesting mini-exhibit in Boston, though we will have a chance to preview the Lawren Harris exhibit that ends up at the AGO this summer. Given that I am trying to pace myself and not totally exhaust the kids, I don't think we will go to more than one art museum a day in New York, which means crossing a lot off the list. I've already decided that the Guggenheim isn't worth it, but it is a tougher call with the Whitney. Just like MOMA, there is always plenty to see at the Whitney, but I am quite bummed that I will miss a Stuart Davis exhibit that opens in June and runs through September. I am a huge fan of Stuart Davis (he's still in my top ten). I think this might actually be worth traveling for, especially since I don't think I will be doing any overnight trips to Stratford this season (probably only seeing Strindberg's John Gabriel Borkman) and the family will probably go off to Chicago for a few weeks without me. If I do make such a trip, then perhaps I would catch the László Moholy-Nagy show at the Guggenheim, though that is a much lower priority. And while I am definitely thinking quite seriously about making this trip, I do see that the exhibit is going to be in DC at the National Gallery of Art in Winter 2016-Spring 2017, which is another strong possibility, particularly if I manage to get a paper into TRB 2017.
Still, one could run oneself ragged trying to keep up with all the art and theatre and concerts in one's hometown. If I seriously scanned everything that happened across Ontario and then the top five or six cultural magnet cities in the US (New York, Washington DC, Chicago, San Francisco, Los Angeles and possibly Philadelphia or Boston), I would just always be sick to my stomach at how much I was missing out on. Better to not look and only occasionally let the major events come to my attention. I guess if I was a paid arts reviewer that might be a different story, but I am an amateur in the strictest sense of not being compensated for my thoughts. I think that covers what I wanted to say for now.
* I had basically assumed I would have to drive, but I forgot that it is worth checking Greyhound and Megabus and even GO Bus. It doesn't appear any of those would work for Peterborough, though I will check again closer to the time, but on the off, off, off chance I go to St. Catherine's in February, Megabus is having an ultra-low fare special.
Edit (1/1/2016): As I was following up on ordering an Archibald Motley catalog that had gone OOP but seems is being reprinted now, Amazon notified me about a new Norman Lewis catalog called Procession. I like Normal Lewis, so I decided to follow up on this, whereupon I learned about a Norman Lewis exhibit, which just opened at PAFA (Pennsylvania Academy of the Fine Arts). While I would love to visit Philadelphia, I doubt very much I can get there before the summer, by which time the exhibit will be in Ft. Worth. I'm a bit bummed out that the touring schedule isn't flipped, since I will be going to Chicago in the summer, but I suppose I can find an excuse to travel to Chicago in the late fall next year. I'm sure my wife would appreciate it if we went around Thanksgiving -- or even the week before or after just to save a bit on airline tickets. (It is worth noting this is a big exhibit -- 90 paintings -- and while the upper floor of the Chicago Cultural Center can hold a lot of art, they still might have to trim it back a bit. Nonetheless, I just can't see making it to Phily this spring.)