Handlebar positioning and posture on Giant bikes
The Cypress is a comfort oriented bike that has a deliberate high handlebar position and upright riding posture. Almost all other bicycle types will have a much lower handlebar position. 

If you look at the Cypress on the Giant website, you can see the bars are above the level of the seat. On the Roam and Cross City they are about level. General handlebar height is built into the geometry of the frame, but the angle and length of the handlebar stem also affects it. Notice that the Cypress has a stem that raises the bar height considerably. 

Handlebar height can be adjusted on most bikes, but only by a a few centimeters. It is possible to raise the bars more by swapping the stem for a 'riser' stem as seen on the Cypress.

The best approach is to visit local bike shops, test ride some bikes and find one that you are happy with. It's always best to buy the bike you actually want in the first place rather than trying to modify one after buying it.

A good bike shop will help you find the bike you want, and would probably be willing to swap the stem on a bike for a riser (if they have one in stock) for a test ride.