"...they would be completely surrounded by the unknown...." Good point!

So where would the wormhole go? One of the dwarf satellite galaxies of the Milky Way? Triangulum or Andromeda? Or perhaps to a galaxy in another cluster of galaxies?
That all depends on what they want to do with the story. I think it would be most interesting if they were somehow transported far away in an earlier time so that they are without a lot of the technology of TNG.
Imagine if a chunk of Federation society was taken out of the TOS timeline and how they would be 100 years later. They might be wearing some derivative of the TOS Starfleet uniform - those that are actually involved in the defense and exploration. The rest would obviously turn to establishing everything the new world/s would need, like schools, government, food production, etc.
They could make an emphasis on more realistic and scientific devices and plot-lines. Without the backing of the federation and the most advanced ships, how exactly are they going to establish a base on an asteroid? How are they going to recalibrate ships to fly in new types of atmospheres that they have never seen before?
The types of aliens would be a part of where they are. If they ended up in another galaxy, it might mean that they are the only humanoids around. Alternately, they might run into another human-like civilization which is structured completely differently, having much more primitive technology in some ways but much more advanced in others. They might even find themselves in a largely hostile new sector of the galaxy, similar to what the Gamma Quadrant was under the Dominion. Maybe their arrival even breeds hope amongst rebel forces who are tucked away in some part of their new galaxy. That may sound like it's borrowing a lot from Star Wars or something, but think about how many times they did this
on one-off planets throughout the whole Trek series.
A good mix of humanoids and more creative aliens would be the best, in my opinion. Did anyone play FTL? There are some pretty creative designs in that game which feel very Trek, but are unique still. They have actual cybernetic organisms that are almost indistinguishable from robots, but are in fact organic. They have reptilian-mantoid things acting as the warrior race. They have pure energy beings. They have metal deficient aliens who do anything to scrap metal and destroy oxygen...and so on. It's pretty cool and kind of inspiring. I like the Engi the best because they are basically good Borg who can reproduce on their own.
http://i1369.photobucket.com/albums/ag239/Hypaspist9/ftl_isotype_zps46fe2a2e.jpg
http://i1369.photobucket.com/albums/ag239/Hypaspist9/780x497_zps397b1cae.jpeg