As soon as you enter Opelucid City, you'll run into Iris again, who remembers you from Castelia City. She tells you about the Gym Leader, Drayden, and also about Route 9 further west. Then she'll walk off. Alright.
Opelucid's appearance changes drastically depending on whether you're playing Black 2 or White 2; in Black 2, it's a lot more high-tech and dark, while in White 2, it's a lot more rustic and lightly colored.
The Pokemon Center is the first building you'll see in the city. You can buy some very useful variants of Poke Balls from the cashier in the second stand. He'll sell Dusk Balls, Timer Balls, and Quick Balls for $1000 apiece. These are all pretty handy for varying reasons. Timer Balls are nicer for longer fights, because after 10 turns have elapsed, they have a 4.0x catch rate compared to an ordinary Poke Ball (as opposed to 40 turns in Generation IV games and earlier). Quick Balls have a 4.0x catch rate on the first turn, so you can use them against a variety of things and can often catch them before the first strike has been dealt.
The first house to the north of the Pokemon Center has a guy upstairs who is a bit of a Tympole Maniac. Apparently he wants to see your Tympole, so if you show him one of yours, he'll give you something — though you can't get Tympole just yet, so come back to him later when you do get one.
The house north of that, over by the closed entrance to Route 10, has some children upstairs that will play a game with you. One will say a Pokemon's name, then three others will say either that name or two very similar names, and you need to talk to the one who said the name the first one called. It doesn't seem to have a point in doing this, though.
To the west of that house is another house. Inside is a lady who gives you another Smoke Ball, which lets the holder run away from any wild Pokemon fight, regardless of its Speed.
West of that, you'll find the Opelucid Gym. You can take it on right away if you want, but there's still more to explore in town as well as on Route 9.
The house south of the Gym has a Gentleman inside who will give you Props for your Prop Case (for the Musical) each day that you talk to him. He'll eventually run out after you've talked to him for enough days, but will give you another special Prop on your birthday (according to what you have set on your DS, at least).
Lastly, Drayden's house in the center of town (just to the east of where you're at now, then north) has an Axew running around in the bottom floor. There's a Football player up top who gives you a Float Stone, which halves the weight of the holder, reducing the effectiveness of attacks like Low Kick or Grass Knot against it, but raising the effectiveness of attacks like Heat Crash when used against it. The girl south of him gives you a Ring Target, which makes it so the holder can be hit by attacks it is normally immune to, meaning if you give it to a Ghost-type, Normal- and Fighting-type attacks can hit it. It's not overly useful on its own (obviously), but can be used in some combos here and there.
At this point, you can either go straight for the Opelucid Gym, or you can take a detour onto Route 9 to pick up some more items and get in a bit of last-minute training!