I visited La Palapa with a friend on a Friday early evening. It wasn't very crowded when we came in but it filled up around 7 pm. It's a small joint - the former site of Thai Me Up - but when filled it wasn't loud. The lighting is warm and the restaurant seems inviting. The staff is incredibly nice. They were really accommodating with seating requests and such.
The restaurant is BYOB and they offered to chill the white wine we brought while we waited.
I thought the food was rather good, especially for Mexican in Pittsburgh. I think this is the closest thing we have to "real" Mexican food within Pittsburgh city limits, especially due to the demise of Mexico City (health code violations = death). The chips were good - they reminded me of the style they serve at Las Velas, but seemed fresher and tasted better than those at Las Velas. The guacamole tasted very good, although I didn't really think about it much at the time.
I ordered enchiladas which were marketed as being able to be served with chicken or beef, but the waiter told me I could have any meat listed at the bottom of the menu (this included chorizo, I believe seafood options, et al.). I chose pulled pork. I thought the pulled pork enchiladas were very well done. The pulled pork itself was moist and marinated well. The corn tortillas (you can choose corn or flour for all dishes - this is great for me, who tries to avoid gluten) seemed really fresh. I've been a lot of places where the corn tortillas fall apart easily, or where they are stale. I was really happy with my meal as a whole.
Another plus is that they will run your credit card at your table with the ipad, and you can choose your tip portion by percentage. I thought that was nice.
Overall - I thought this was a great dining experience.