Nearly all of the miniquests are doable for new players Apart from the Evil Dan mini quest series.
Most of them can be found in lumbridge and varrock, and some in falador. There are several others in quest locations (port sarim, draynor, taverly), but they offer no reward whatsoever.
Lumbridge ones are pretty solid, with decent weapon- and armour rewards, and some wc, ranged and cooking exp for starting out.