f/5.6 is pretty slow. Still, the f/5.6 lens you have with you is better than the f/2.8 lens that you have at home. With a tripod, it's less of an issue of course.
Depth of field control is still an issue - you have more ability to do that with an f/2.8 or f/4 lens.
I have three Nikon lenses in this range:
80-200/4.5 (AI-converted) - I picked this up cheaply based on its reputation of being a fantastic lens. Zoom lenses have improved since then but the lens isn't too bad. I'd call it average in quality. (I could have a below-par sample.)
70-210/4.5-5.6 AF - this is my "city" lens for when I don't want to carry a big lens and I'm very happy with it. The f/5.6 maximum aperture at the long end is a little limiting, but when you can live with that the results are very good.
80-200/2.8 ED AF - amazing, but big and heavy.
I don't know how good the AI-S lens you're mentioning, but the AF version is certainly excellent.
If I were going to get a manual-focus lens in this range, I'd give serious thought to the 80-200/4 AI or AI-S. It's still inexpensive but it has a great reputation.