It was at the Friendly Arm Inn, right outside the entrance of it. The place where you find Jaheria and Khalid. The biggest problem I had with the assassin was that he kept paralyzing (IIRC) my characters, so I found that getting Jaehira and Khalid first helped in taking him down. Of course, I usually make a fighter or a fighter/cleric in those games, so an archer or a mage might be a bit better in that situation.
And the pause option can be quite critical in some encounters, and especially practical if the movement pathing messes up.

A tip is to bring the insane ones (Montaron and Xzar) that you meet near the end of the road at the first area, then leave them at FA and replace with Jaheira & Khalid if you're planning to be good. That way you'll have 4 people (including yourself) if you brought Imoen along (I do know some who just leave her... barbarians!), and the fight shouldn't be hard to come through alive.

Yeah. Immy is my favorite character in the series. Bar none. I mean, I'm aware people leave her behind because she's like a chipmunk on a constant sugar rush, but she's just too darned cute, and... well, she's family, so... (Shrug)
Anyway, it's true, the bit at the Friendly Arm is just sickeningly frustrating if you don't know what to expect (which you don't.) Bringing Xzar and Montaron along helps sometimes if only because that assassin mage usually hits you with a Fear spell which sends you flying off in a blind panic (you're so weak you almost always fail your saving throw) and then he just has to paste you with a single spell and BLOOP! You're dead.
At least with the extra party members, you can distract him or something to make sure he doesn't get those spells off. Basically, just "surround & pound" until he goes down. And then, yeah, once he's down, you can give the creepy halfling (Even though it's Earl Boen being awesome.) and the creepier necromancer the boot and replace them for Khalid and Jaheira.
Problem is, most people when they first meet Xzar and Montaron will probably be all "These guys are seriously not right in the head" and will just give them a pass, which is basically what I did since... they were SERIOUSLY NOT RIGHT IN THE HEAD. :D

My problem with the two candlekeep assassins was that I used to play as a Mage, and a lvl1 mage is awful in BG1, since you have 1-2 spells and then you have to sleep.
My first play through, I killed the first assassin with either a magic missle or flaming hands, and then met the second assassin who promptly stabbed me to death because I no longer had any spells, and was useless with a staff.
The key thing to get past the FA mage/assassin is to draw him out towards the guards that are not far from the stairs. Then, they will help kill him.
edit: Theres also a very nifty Ring of Wizardry (extra spells per level) to the left of the path at the bottom of the FA map. Very hard to find, but I managed to get it with the Tutu mod, because in BG2 you press TAB to highlight chests etc.

Great tip!