So I can vouch for
http://www.lotuselectrolysisseattle.com/ and I've heard good things about
http://expertelectrolysis.com/ as well but I really really think you should do laser first if you want to save money.
Laser is considered permanent hair reduction while electrolysis is permanent hair removal. People (including myself at first) misunderstand this. Laser actually removes some hair permanently as long as it is dark hair against lighter skin and the proper laser (Nd:YAG is usually what you want to look for, IPL isn't always effective, Alexandrite is good for large areas, etc.) is used.
I guess the best example would be something like if you had a 100 hairs on your face, after about 10 sessions (11 for me) You would probably permanently lose 70 of those hairs. The rest that are either resistant or keep coming back (hence the wording of permanent reduction v. permanent removal), etc are the ones you want to finish off with electrolysis. 10 sessions with groupon would cost maybe about $600 or so and if get laser once a month, it would take 10 months to do.
As for electrolysis, you would need to spend an average of 200-300 hours for a full clear. That means at the median price of $70 per hour, it would take about $14,000 to $21,000 for a full clear. Anyway, that's my thought on it.
As for me, I've had 11 sessions of laser before I had to move to electrolysis. So far, I've probably have only had about 14 hours of electrolysis and don't really have that much left to go. Just remember that hair can only be killed during the anagen phase (active growth) if it is in the catagen or telogen phase, it'll grow back. Anyway, hope that helps!