If I want to say "the amount of tourists" as in "It doesn't feel remote because of the amount of tourists that come", what should I say? I'm wondering whether to write "an méid turasóirí" or if the tuiseal ginideach would make it "an méid turasóir"... Basically I'm confused!

For the full sentence I have written "Ní bhraithníonn sé iargúlta dá bharr an méid turasóir(í) a thagann ó chian is ó chóngar", but I'm not sure if any of that is correct either!

I'd be very grateful if anyone could help me!
Go raibh míle maith agaibh

It doesn't make a difference here because the genitive plural of turasóirí is again turasóirí (as it is in all strong plurals)
so: an méid turasóirí

Another case are weak plurals,
eg. fear - fir.
Here, genitive plural is fear
so: an méid fear

But it is: de bharr an mhéid turasóirí (not dá; lenition of méid)
and: Ní bhraitheann sé go hiargúlta (the verb is braith, not braithnigh - perhaps a confusion with breathnaigh = watch or breithnigh = adjudge?)

Thanks Labhrás. That helps .
One further question please:

I wanted to say'' it doesn't feel remote because of...''/ ''doesn't seem remote''

how do I say that ? I thought in the end it was better to say

''ní cosúil gur áit go hiargúlta é...''

Indeed, I did get confused with ''braith '' and ''breathnaigh'' . I am not sure the sentence makes sense using these.
Go raibh maith agat/agaibh

... áit iargúlta ...