Ndtyhij

No idea why my dad dragged me into this place. Some guy is performing on the stage. He's reading numbers out loud. I think it's some kind of a sequence puzzle.

1... 8... 9... 16... 17... 24... 25...

This is boring. Where is this place, anyway? Yorkshire or something? Everyone else is quiet. I bet they're concentrating on figuring out the pattern.

32... 33... 40... 41... 48... 49... 56...

I'm pretty sure I have this solved already. I won't spoil it for anyone just yet, though. I think somebody else will figure it out soon as well.

57... 64... 65... 72... 73... 80... 81...

This is so simple. How is nobody telling him the answer already?

88... 89... 96... 97... 104...

Everyone's clapping now. Is it over? He's gotten to 100 and nobody guessed it? I better clap as well.

105... 112...

Wait, it's continuing? Okay, he's giving us another chance. I see where this is going. The next number is 113.

113...

And then 120...

120...

This is a nice opportunity to impress my dad. I lean in and whisper to him that the next number will be 121.

(...)

I was wrong?!

What is the next correct number in the sequence? Why do you think I'm not able to enjoy the performance like everyone else?

I think that the next number will be

122

Because you are watching

A snooker match (potentially at The Crucible in Sheffield)

The numbers are called out by

The referee, when declaring the size of the break (the score accumulated so far without missing a shot). The sequence of numbers suggests that the current player has potted 15 red balls and 15 blacks without missing and it's still possible to achieve the maximum 147 (very rare in snooker). The next ball will be the yellow ball which is worth 2, taking the score up to 122.

NB In professional snooker matches, it is normal for the audience to applaud when a player reaches a century (surpasses 100) so this would certainly happen in your case.

Addendum

As pointed out by celtschk, the author may not be able to enjoy the performance due to blindness or some other visual impairment.

To clarify about the rules of snooker, when a player comes to the table the aim is to pot a red ball, worth 1 point, followed by a ball of any other colour (yellow=2, green=3, brown=4, blue=5, pink=6, black=7) and proceed alternately in that fashion. Red balls are not replaced when potted, while the others are. Once all 15 reds have been potted, the aim is to pot all the other colours in increasing order of value. On this occasion, they are not replaced once potted. Thanks to zakinster and bornfromanegg for addressing this.

To address the one part that hexomino didn't already answer:

Why do you think I'm not able to enjoy the performance like everyone else?

My answer would be:

You're blind.

This is hinted at by the fact that

while acoustic observations (like everyone being quiet) are given, no optical impressions are, which is atypical for someone able to see. The fact that you are unsure about the location may also be a hint. And finally, it explains why you didn't see the table.

You are not able to enjoy the performance because

you are blind, all of the descriptions are of sounds, not sights

Just a small nuance / addendum to the already good solutions posted so far.

You're potentially

Watch... errr... hearing a perfect snooker frame.
So far the player has been potting, alternately, a red ball (worth 1 point) and the black ball (worth 7). Instead of black, the player could have potted a ball worth less points, but then she would not be going for the perfect game.

If all goes well,

the player, after cleaning the red balls off the table, will be potting the other balls in order, from lowest value (yellow) to highest (black).

Therefore, the full sequence is:

122, 125, 129, 134, 140, 147

In addition to everything else...

There is a clue in the line "Where is this place, anyway? Yorkshire or something?" As the most famous place to play snooker is The Crucible which is in Sheffield, Yorkshire.