I've been using Elise quite a lot in Dominion recently. She's incredibly good at bursting (AP) and makes a fine bruiser aswell.
I used AD bruiser when she first came out but since then switched to AP and was surprised at just how much damage you can get when you stack plenty of AP with magic pen. The main key to playing her is combo speed. If you can pull off what combo's/tactics you need to quickly enough then you can pretty much win any fight.
I tend to build mpen boots, blackfire torch, wooglet's, abyssal, rylai's and whichever item you want (game's normally over halfway through rylai's). You end up with about 20% damage on your Q.
Elise doesn't really struggle against anyone as long as she gets enough poke in. Champions that really give her trouble (in my experience) are singed ("let's not die to anything!" - constantly poke with Q, level W if bot to wipe out creeps in one blast to stop him pushing), Kassadin (trollteleport - basically use other champions to pile him or make him blow his first teleport then burst), Garen (tanky, but this is really that I struggle against him personally). Her worst nightmares are silences.
She absolutely demolishes squishies, can take bruisers head-to-head, and provides solid damage against tanks.
AP burst combo - E-Q-W-R-W (auto-attack)-Q
R then Q can finish off the enemy if they have around 200-300hp left (you should combo and have around half a second left on your human Q by the time you can shift back).
Final note - plenty of people have the "KILL IT" mindset when they see a champion with low hp. If you're low and sacrifice yourself to allow a team mate to recapture a point then you can Rappel then go straight into stasis to waste an extra 4 seconds (5 if you stunned the enemy aswell!)
Just my $0.02