Anyone can indeed attend a tisch. I have done so myself numerous times, and I am not at all Chasidish. However, make sure to follow protocol (which is mostly just common sense) so as not to annoy or offend the participants.
It should be noted that Satmar is a particularly insular sect of Chasidus, and while I’m sure they will in no way object to you attending their events, it may pay to start by a more tourist-friendly group. However, as I have had very little exposure to the gongs-on in BP, I cannot suggest any group in particular myself. Maybe somebody else here can…