I need to pick up a few things on the way back to the hotel . Feel like stopping at cosmetics store ? We could get some makeup .

I need to buy/obtain/get a few things on the way back to the hotel.
(Please pick up some milk when you go to the supermarket.)
(I picked up some Carioca slang last summer while I was in Rio.  [to pick up = to learn without formal study])
(She picked up a cold while on vacation.)
(Where did he pick up that strange accent?)

Feel like = Do you feel like (informal)
(Do you) want to go now? (informal)
(Do you) love me? (informal)
(Does he) care for more coffee? (informal)   

I'd like to, but I think I'll pass .I don't have much time today .
I'd like to, but I think I will decline (not do it, accept the offer).

("To pass" is a poker term.  It means "to take no action, not to make a bet, not to do anything.) .

John:  Would you like more coffee?
Jake:  I'll pass.  (No, thank you.)

From this context I draw the conclusion  that is something like " vou deixar para a próxima vez "  but I'm not sure since I didn't find this meaning at something written .
I agree with your translation.

another question : Why in the sentence Feel like ... there is no auxiliary verb ?
Informal English.  See above.