I would use "CHECK IN", It's better in this case!
Check into is more to mean:examine so as to determine accuracy, quality or condition, example: Check the brakes; check out the engine.
Check into would be synonym of: check, check up on, look into, check out, suss out, check over, and used as an hypernym will mean: analyze, study, examine, as an hyponym means: watch, observe, follow or keep an eye on.
I think the "Check in" is the best in this case because: we can define it saying: check in is the process of announcing our arrival at a hotel, airport, etc. When we are in a hotel we can read the sign called "CHECK IN"