Handlebar positioning and posture on Giant bikes I currently own a Giant Cypress. 

I am looking at buying a new bike. I tried someone's Giant Roam. Although the seat height was a bit low for me, I felt like I was falling forward on the bike, whereas on the cypress I feel a bit more upright, which I prefer.

Is this just the design of the Roam? the info sheet says "Giant Connect, Low Rise" handlebars

So also looking at the Giant Cross City, wondered if that would be a bit more upright. 

If the lowness of the handle bars something that can be adjusted? Or can I achieve a bit more upright positioning by getting a larger frame and setting the seat height on the low side?

Any advise would be appreciated.
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.