Is this your very 1st cell phone? I can assure you this is a market wide issue regardless of phone brand, carrier, smartphone/dumbphone, yearly income, social status.... it doesn't matter really, buildings have always and will always cause problems with cell devices. Unless there is some sort of signal booster implemented in the building.
Thats not to say there's no difference from one phone to the next as far as getting service inside a building. But service in certain area's will effect all cell phones, not just the Droid X. I've always found it to be more of a carrier thing myself though. Like for instance where I live Verizon just has better coverage than all the others. Believe me Verizon was my last choice because they are by far the most expensive carrier around here. But after initially signing up for AT&T (back then they were Cingular), tben switching to Sprint, I eventually had no choice but to go with Verizon because I got sick and tired of having to go out and stand on my front porch at my house (especially in the winter) just to get a single bar of service. And that was the same with all 3 phones I tried out.
Switching over to Verizon has been absolutely worth the larger monthly bill. Now I get service practically anywhere I've ever been (buildings excluded).