With Gene Rodenberry's blessing, they did just that.
Don't expect anything fancy. It's just a little storefront museum of memorabilia where they sell t-shirts (I bought one for a Trekkie friend). There's a yearly Trekfest and birthday party in March. I don't think it's as big as it used to be, but if you are a big Trekkie, it's probably something you should do once if you can.
Across the street is a playground and picnic area. Eating places are scarce, so bring a picnic lunch and relax.
The monument itself is down the main street (there really is only one in the town). A banner points to a small alley between a beauty salon and the main wall of stores.
Behind the beauty shop is the monument itself. I suppose it will be more hospitable to birthing babies in 200 years or so.
Nearby: Iowa City on I-80 (25 minutes north On US-218), Kalona Colony to the west. This is Amish country, so ask the locals where to get some yummy baked goods, and watch out for buggies.