City cyclists can ride at an easy 12mph pace with no sweat. You can cover 4 miles in 20mins. Going a little faster will get you there a little quicker but you will have to wait to cool down so there is no gain.

You can use almost any bike for easy-paced city riding, road, hybrid, MTB, utility/commuter, folding.
Make sure the bike has enough clearance to fit wide-enough tyres and if it gets wet, fenders. You will want fittings (threaded eyelets) for a rear luggage rack and fenders. Even if you dont fit them , eventually you will so its better to have the eyelets.
You dont need suspension but most mass-market everyday bikes come with suspension forks.

If your city has steep hills you need low gears.
Where will you store or secure the bike? Do you need something to carry up to an apartment and small enough to keep inside?

I would suggest an entry-level hybrid style bike from a respected brand, these are cheap, easy to find and can do everything you need. If you get more ambitious then you can get a higher performance play bike for the weekend.
Road bikes often lack the lower gears, they have high ones for racing. Some do have lower gears and are OK to use but lack wide tyre clearance.
Touring bikes are excellent doitall bikes but you dont get cheap ones, they are harder to find than hybrids. Some of the modern cyclo-cross bikes are more like tourers with useful eyelets and features.