Personally, I've never heard of "grab" as in learn, but "grab" as in "get" or collect is informal, yes. This is a definition from Wiktionary of "grab", and one of its usages, the one that seems to apply to your context, has been dubbed informal:
(informal) to quickly collect or retrieve
Grab, is an informal word, and presumably not advised to be used in your situation.
If that person is a kind of respectful, dignified person, than just simply writing "I"d like to invite you to somewhere where you will be able to acquire a lot of cultural and historical artifacts" would be better.
Or, if the object was not an artifact, but learning, then, perhaps try:
I would like to invite you to a place where we would be able to increase our cultural and historical knowledge