Something like two thousand visitors come here every day. यहाँ हर रोज हजार के आस pass visitors sate hai... Something ki jagah ... Around the toh Nahi aayega.

No! Because around means, " चारों ओर" and here should come the sense of "लगभग". So you can write it:- Almost/Approximately two thousand visitors come here every day.

I think we can use 'around' here because in modern english around is also used in the sense of 'के आस-पास' or 'लगभग'.

I think we can use around but approximately is more better than around

Around two thousand visitors come here. May be right.