Take a look at Panicum virgatum 'Northwind.' It's by far the most upright and erect grass I've seen.

If you'll be using pots, and can winter it over indoors, Juncus 'Javelin' is another possibility.

"Also: I over wintered some grass in my basement and they look good. But, can I cut them back and will they grow tall again?"

What sort of grass?

Panicum 'Shenandoah' is one of my favorite grasses - medium height, pretty delicate flower heads, and doesn't flop at all. Mixes well with many medium height perennials. Doesn't get much color in the shadier locations though.

Other tall grasses that grow upright for me - Miscanthus 'Gracillimus', Miscanthus purpurascens, Calamagrostis Karl foerster and Overdam, other Panicum virgatum cultivars (Heavy Metal, Rostahlbusch). Panicum 'Cloud Nine' is very tall and flopped a little, perhaps because it was growing in partial shade.