Dude there are *four* surviving space shuttles. One in DC, one in NY (those are close together, fair enough -- the one in NY was only for atmo testing and while mostly capable of flying in space, but never received the refit to be able to do it) but the other two flown shuttles are at KSC in Florida and in Los Angeles. If your argument was that people have to travel too far, then we'd move the NY one to Nebraska or something to minimize distance traveled from any point in the country. That would also be a lot cheaper to stay at a hotel there than in Houston.
But, conveniently, Florida, New York, DC and California are some of the most visited places in the US. 64% of Americans have visited Florida (far more than any other state), 56% have visited New York, 54% DC, and 50% California. Texas just barely beats California at 51%, so you could probably improve accessibility a tiny tiny tiny bit by moving the LA one to Houston, but that would leave the entire western US with worse access (distance from LA to Houston is 1500 miles, vs distance from Houston to KSC is 1000 miles, and that's not even taking into account places like the Pacific Northwest.)
If you want to see a shuttle for less money, you have a couple of options. Go to Florida and drive to KSC, or stay at a cheap place somewhere along the Northeast Corridor or Metro North train lines and take a day trip into NYC -- you can stay late as the last Northeast Corridor trains run late into the evening and the Metro North trains leave as late as 1AM. (And you can take an uber to Penn/Grand Central to get the short distance to the train stations if you want to avoid the subway at night -- it's not as dangerous as the news makes it seem but you do see some tweakers on the subway, but the regional trains out of the city are clean and comfy)