Depends on what you're trying to do. If you're trying to look pretty then get some ugly colored bits and have at it. Looking hip is not my thing. I built my bike to go fast on a budget. Everything below is assuming you're already comfortable on your bike. If you're not comfortable then you need to address your cockpit and saddle first. I prefer road drops with double brake levers (modern style), gives you a many hand positions but bullhorns are good as well. My favorite saddle is the Sette Nyx, an amazing lightweight (and inexpensive) saddle but very narrow.

Wheels may run more than $150 for good quality depending on what you want but will make the biggest most noticable difference depending on what you have now. I run these on my fixed (they were stock and I see no reason to replace them). They're pretty good. Not the best but they're strong enough for my Clyde frame and roll really well. If the bearing ever wear out, for less then $20, you can put ceramic Phil Wood cartridge bearings in and they'll roll as well as wheelsets that cost twice as much.

Next, tires. If you're skidding - well their are lots of threads on that - have fun searching. Otherwise I'd tell you to expect to spend $30-$50 per tire on the best tires you can find. I'm actually quite happy with the 23mm Hutchinson Fusion 2 Ultras that I got super cheap on Bonk Town. They're really fast rollers when aired up but wow they drag like wet cement if they're low on air. Which ones are right for you will depend on where and how you ride.

If you have decent wheels, the next place I'd look is cranks and/or bottom bracket. I'm running the stock FSA cranks from my bike. They're good enough but they're on my list of things to replace. My bottom bracket definitely needs to go. My fixed is the only bike I don't have outbound bearings on. My opinion is that outbound bearings are massively superior. But it's just an opinion and there are people that hate them. I think they look better and perform better. I'm thinking about these but I'll probably just replace the bottom bracket and keep my current cranks since they're plenty stiff and dropping a bunch of money into something that isn't broken would be antithetical to what I'm trying to accomplish with this bike.