It depends on what you want to say.

It’s perfectly acceptable to say : “Je suis touriste ici”, meaning that you have a “tourist” status, as opposition to a “resident” status. However, this is really situational, and the most commonly used sentence is “Je suis un touriste”.

@Al_th, that’s funny. For me it’s the opposite.

“Je suis touriste.” perfectly fits the situation.

“Je suis un touriste.” is more used to tease poeple, to say that you’re some kind of amateur, beginner or something. For instance, if I play badly soccer/football, my friends will tell me “T’es un touriste!”. Just teasing for fun.

So if you say “Je suis un touriste” to someone in France (I don’t know about Quebec), I think people will laugh a little.

As far as I know, touriste is a noun not an adjective. So “je suis un touriste” should be preferred in my opinion.
It can also be used as adverb in “en touriste”.

Both are acceptable.

They are almost interchangeable, but I personally perceive them a bit differently:

« Je suis un touriste »: I’m a person who is a tourist. The kind of people who wear short pants, crocs, take many photos and buy a lot of garbage. Also an easy target to rob.

« Je suis touriste »: I’m here as a tourist. Kind of voluntarily lost, flying in the clouds. Doesn’t belong to this place, doesn’t plan to stay in it. Easy target to rob, too.

A late answer but anyway I wouldn’t recommend in your case either Je suis touriste which isn’t idiomatic or Je suis un touriste which can be perceived as slightly amusing as already stated.

What I would suggest would be to simply say Je suis en vacances ici. I’m sure your accent will implicitly show you are not a native French speaking person. Note that many tourists in Montreal are still native French speakers (eg from France, Belgium, Switzerland or other areas).

PS: I guess you really wanted to make clear you are not a native francophone, not anglophone as you wrote.