Hybrid / city / multi-use bikes now come with both styles of handle bars. 

Not endorsing this bike.  It is just an example.    
[MultUseWithDropBars][1]  

One thing to consider is a cyclocross and put touring tires on it.  It has drop bars and will take larger tires.  You can get great deals on used as many racers upgrade every season or two.  


  [1]: http://www.specialized.com/us/en/bikes/fitness/awol/awol