Besides Whiterun, what is a good starting city for a new character?

Solution 1:

I walked to Falkreath with a lvl 1 character, then with about a lvl 5 went to Markarth. The only time I had problems was attacking a fort on the way to Markarth, the forts and villages were to high a lvl, but then I just skipped them and did quests in Markarth. Didn't touch Whiterun till lvl 20.

From what I've seen most cities are scaled per lvl, the surroundings might not be fully scaling but you can avoid things that'll kill you.

To answer your specific questions:

A surrounding wilderness free of Sabre Cats, Bears, Frost Trolls and the like

Falkreath has none of those

Some nearby camps/dungeons accessible to characters below level 10

Falkreath as well has about 5+ dungeons you can walk to, on the way to it from the starting area you run across some dungeons you can do at lvl 1-2

Markarth has a number of near by areas but seems to be more for a bit higher then lvl 1 or 2

More than one side quest to pursue

Falkreath has bout 5-7 side quests in the town, depends on how much follow up you do with them.

Markarth has a lot of side quests