I've found that most crossfit boxes have closed up and the ones that are still around have had to drop the elitist attitude and incorporate trainers that actually know what they are doing and also have scaled back the 'weight against time' mindset. The ones that are around seem to have smartened up and coincidentally, you don't hear about injuries as much.
So, OP, find a good one or learn the oly moves and they are a great addition.
Also, don't necessarily look for ones that use "crossfit" in the name because the method of training isn't unique at all, but the name requires heavy dues to use it and it is generally passed off to you and not on paying good trainers. You are after oly lifting basics that you can find many places.