Synonyms for Check out:

n.

look around, take in, gaze, check on, look, stare. scrutinize, study, monitor. homestay, late checkout, patron, booking, bookable, book in, guest, check-in. borrow, depart, take, get off, co-opt, run away with, leave, pay, pawn, leverage, settle up. browse, inspect, hit the town/street, etc., put something on the slate, shop around, shop, appraise, verify, change, price, examine, take back. measure up, come to life, go without saying (that), ring true, exist, be witnessed by something, hold true. check out (noun)
go over, Suss Out, check into, check over, feel out, check, check up on, sound out, look into, cheque.

v.

examine (verb)
inspect, verify, appraise.
leave a hotel, hospital, etc. (verb)
leave, settle up, depart.
prove accurate or consistent (verb)
measure up.
stative (verb)
check.

Other synonyms:

book in, late checkout, bookable, shop around, examine, homestay. shop, check-in, booking. patron. price, take back, depart. guest. change. ascertain
check up on.
case
check over.
look into
look into.
qualify
measure up.
suss out
Suss Out.
Other relevant words:
inspect, appraise, get off, verify, look, settle up, monitor, measure up, study, depart, scrutinize, check on, examine, leave.