The suits of the cards are irrelevant.
25c 50c 6max online cash game.
IDK how to post hands with pokertracker but this will do.
How can I play this hands better? What's wrong with my thought process?

Hero has 120$
Villain has 90$

Fold
Fold
Fold
Hero K10 in the button raise to 1.50$
Villain in the SB raise to 4.50$
Fold
Hero calls.

Pot 9$, Flop : A-10-10
SB checks
Hero bets 5$
SB calls

Pot 19$, Flop A-10-10-Q
SB checks
Hero bets 8$
SB calls

Pot 35$ Flop A-10-10-Q-J
SB checks
Hero bets 15.50$
SB raises to 53$
Hero calls.

Villain shows Q-10

Thought process : Love the flop hopefully an ace can call my bet, I really don't like the turn but it looks good enough to value bet anyway, hate the river, now it feels like I only chop at best here. With the huge raise, it feels like I'm against a full house most of the time. I give him J-10 or Q-10 a lot, but it sucks so much with all the money in there but more importantly, that I flop gold and the turn river are disgusting, I guess I could be chopping here or good so I call, but I take a long time heavily thinking to just fold.

In retrospective, I guess I can just check-call the river since it sucks, but maybe I'm missing value, I don't know. If it turned out like A-10-10-7-4 I would have happily be thinking to put enough money to have max value/all in, but this river I can only fold or call. With a A-10-10-Q-7 flop, I can only call his raise, maybe fold, I'm not sure, probably calling and feeling awful about it, I think he represent a full house with that river raise, like, always?... 90% of the time?....

Deep stacked 50NL 6max is not a beginner's stake

Check it back OTR. Villain isn't calling with much (if anything) that you beat. Tx that doesn't make a str8 or a boat doesn't make much sense for him.

Suits matter. Knowing suits helps define villain's range.

Agree till the river. Then it's check-check for me.
There's only one 10 left So only 3 combinations JT and 3 of QT.
However, his range contains AK, AQ,AJ, JJ+ and possible even KQ and KJ (since you raised on the button your range is pretty wide and consequently his 3-bet range can be wide also to attack your trashy hands)
Which hand - that he's still holding after you betting 3 streets and that will call on this board - do you think he could have from which you could extract value?
AQ? AJ? Not likely.

PokerStars - $1 NL (6 max) - Holdem - 5 players
Hand converted by PokerTracker 4

UTG: $93.70
CO: $284.00
BTN: $132.85
SB: $99.00
Hero (BB): $91.05

SB posts SB $0.50, Hero posts BB $1.00

Pre Flop: (pot: $1.50) Hero has A A

fold, fold, BTN raises to $4.00, fold, Hero raises to $13.00, BTN calls $9.00

Flop: ($26.50, 2 players) J Q 6
Hero checks, BTN checks

Turn: ($26.50, 2 players) 8
Hero bets $15.00, BTN raises to $119.85 and is all-in, Hero calls $63.05 and is all-in

River: ($182.60, 2 players) 9

Hero shows A A (One Pair, Aces)
(Pre 93%, Flop 91%, Turn 95%)
BTN mucks A Q (One Pair, Queens)
(Pre 7%, Flop 9%, Turn 5%)
Hero wins $180.60

You didn't play it badly. My thought process would have been very close to the same as yours besides the River. That would have made me really second guess my initial feelings also. I also agree that a Check on the Turn would have been good too. It also really depends on how the villain was playing up to this point...Is he a Reg? What was your overall feel as to what type of player he is? All of that plays into your decision for sure (which you already know). I would chalk it up as a Bad Beat and learn from it...Move on from it. I don't think you did anything wrong here, I think you played it right, you just had the worst of it. And yeah, suits definitely matter.

We have all felt the wrath of a "Bad Beat" my guy (Multiple times a day lol), Learn from it, Study from it, and come out on top.

Good Luck Man!