No, you are not stuck with the vintage look. However if you change the wheels to something more modern then you are putting yourself in the position of needing to update numerous other things on the car to meet and match the look you are then going with.
You have a car there in good condition. If your car needed a paint job and interior and everything done, then it would be just a matter of matching up all the looks to the theme you are looking for.
I am a big fan of setting a theme and sticking with it. Nothing bothers me more than to see someone spend tons of money on good parts that do not match a theme or look and then they have a car that looks like a mismatched hodgepodge. The top hot rod designers are masters of getting the look and theme right. The local punk kid often does it all wrong. Remember the last time you saw a stock minivan with very modern 20s on it and rubber band tires? Looks weird huh?
Have you ever wondered why that 65 Shelby clone always looks so sharp? It's all old technology, all following an old pattern. That's because it's a classic look that is accepted by everybody.
It is your car and I don't want to tell you what you should do with it, however I don't want to see you start spending money at random and going in circles trying to figure out why you are not getting where you want to be. Take a look at the cars that some of the members here have, some have done a great job of hitting the target for looks of a theme. Look at the Internet and magazines and find the look you really drool over. Then look at your car and see what the difference are. That is the beginning of setting the theme that you want.
Also remember that you can go with a modern theme with modern wheels. After a few years or a decade that look could be gone and you may be wanting to change the car again. How many 80s hot rods have you seen in great hardly used condition but look totally out of date?
One benifit of the vintage look is that it already went out of style and has come back to stay. Odds are that vintage look will never go out of style again.
So as I am dragging on, it is your car so do with it what will make you happy. However consider this. If you are going to start throwing money at the car to change the look, how about getting a different car and start to build in it the image you have in your head. In the end you could end up with two badass cars that each have their own personality