Hero ($320) - UTG+1 - mid 20s TAG
BU ($240) - mid 20s, aggressive but not thinking player
SB ($440) - mid 30s, solid thinking player

OTTH
f, Hero UTG +1 QQ Raises to $16, f,f, HJ calls $16, f, BU raises to $60, Sb calls $60, Bb folds, Hero ??

I call $44, HJ folds.
Flop (Pot $198): 974
Sb checks, hero ?? I check, BU jams ~$180, Sb All - in covering us both.

I folded but thought about it later and asked myself why I am calling pre if im check folding to one of the better boards for queens. Flop should be b/f but I was convinced one of them would have better hand considering 3bets are rare let alone cold calls from blinds. Any thoughts on navigating this mess of a hand?

Pre too big, I would just rip it in pre or fold pre if you think BU/SB are nitty.

"Any thoughts"?

Yes. Range your villain properly after the 3 bet, and then proceed accordingly like Minatorr also mentioned. Calling the 3 bet pre only to fold on one of the best boards for your hand (as you wrote yourself in the OP) its just lightening money on fire.

If you range your opponent heavily on KK/AA, then you have exactly 2 winnercards and should just fold pre.

Do we think that button with 3bet TT here?
What about 99?

Will SB be colding here with all pocket pairs? Only TT+? 66+?
AKs? AQs?

Without these questions we can't give you the best answer, but generally you're beat by one of them here given the preflop/flop action. Fold.

Shove or fold pre.

I did range my villains hence the fold OTF. It's not that I was concerned about the Bu 3b but most concerned about the Sb cold call. Should have just folded pre, it was a leak

Bu 3b range likely TT+ AQ+ but the cold call from SB is likely JJ+ given he would probably 4b jam AK oop??

Does BTN three bet a lot? Assume he can three bet light given description. If so I probably shove pre. Generally BTN is capped by cold calling at something like JJ/AK. It's rare for someone to cold call AA or KK.

Not sure you could have done anything less correctly in this hand.

1. You need to balance your preflop range. You're not often getting value with an open of 8bb.
a. Worse hands fold; better hands and coinflips call.
b. If you open for less, you widen your range, allowing you to (i) see the flop with worse hands when you have them, (ii) get value with premium hands, and (iii) induce a 3-bet so you can 4-bet/jam your premium hands.

2. What are you hoping to see on the flop?
a. No overs came. (i) If you're gonna fold assuming an opponent has AA/KK, then why did you call pre? You lose 80% of the time against those hands. (ii) AA/KK is the damn top of BTN range, so you're crushing a majority of his realistic range of ATs and better. When sb calls the jam he's got a pair, 77+.

b. Had you 4-bet pre (3.5+ times the 3-bet), you could eliminate a chunk of BTN range or else ended up contending only one opponent, where the flop becomes much more relevant. Check the flop against an isolated opponent and see his bet size if you understand how sizing indicates range post flop, but I don't usually play this way. I'm always 4-betting/jamming with the 3rd best hand from a more standard UTG open because you're rarely losing in this spot.

How'd the hand play out after you folded? Also relevant info...

Wat?

Do you have a specific question?

Sure, I'll give you a chance.

Why is anything that happens after we fold relevant to what we should have done at the time we are making our decision?

Not relevant for the current hand (nor the most important part of the post), but if you're going to characterize these players you could use this hand's info to facilitate future hands.