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

Not endorsing this bike.  It is just an example.    
[MultUseWithDropBars][2]  

One thing to consider is a used 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.  And this is end of cyclocross season. 

This is a cyclocross set up with 35mm touring tires that I use for training and crashing around the city.

![enter image description here][1]


  [1]: https://i.sstatic.net/U3LUx.jpg
  [2]: http://www.specialized.com/us/en/bikes/fitness/awol/awol