A good place with a chance to see both species is Craigellachie NNR just to the west of Aviemore.
http://www.nnr-scotland.org.uk/craigellachie/
It's a beautiful reserve with a huge variety of insect life, as well as plants and quite a few birds. For example it's one of my best local spots for Wood Warbler. Moths, Butterflies and Dragonflies are also in abundance, particularly on sunny days. You can also see Frogs, Toads, Palmate Newts, Lizards and Slow Worms.
The best place to see the Frits and Green Hairstreaks is by following the Viewpoint Trail, which is steep in places, up past a large, flat water tank to a more open area just above the tree line. If you follow the trail up past that to the viewpoint and then to the top of the hill there are fantastic views over Rothiemurchus Fish Farm to the Cairngorms. It's a bit of a slog though.
In general, for the Frits, you're looking for south-east to south-west facing slopes with bracken with plenty of Violets, the larval foodplant, and Bugle, which the adults seem to like nectaring on.
Green Hairstreak seem to like woodland edges with plenty of Blaeberry, I've seen them on the Speyside Way, the section between Aviemore and Boat of Garten.