I would suggest, well, a few things. Maybe. If you want drop bars, then that opens up lots of other possibilities. I'll speak toward the others.

First of all, yours are fine, but probably waste a lot of energy. If you're ok with that, with the workout and all, then you are fine. But I would definitely get slicks or semi-slicks.

Second, an older, non suspension mountain bike would seem perfect, with the same tires mentioned above.

Third, someone mentioned the Trek FX series. That does seem perfect. If you really want to buy a new bike, something like that would be great. There are other manufacturers who make similar products, but I own a 7.3 FX, and it's great. I also own a Felt X City, 2009 model, which is a wonderful bike. The others I can't comment on.

So, if you are itching for a new bike, I'd say a hybrid (like the FX series) would be a great choice. Still have pretty wide tires too. If you want something with drop bars though, I'll let the people with more experience offer their opinions.

Good luck!