Hi, Vel. I think that the Depot Bench and Central Rim areas are great. If you can find something in the Waterfront District in Garden City, that would be fantastic, otherwise, the rest of Garden City is not where I'd expect to find a lot of young professionals. The nice parts of Garden City which sit between west Boise and northwest Boise in the area around Glenwood and the Boise River, are heavily populated with retired folks and families. The Waterfront District is a new area in Garden City that is next to the river in the easternmost part of Garden City that is next to downtown. In-between these residential areas, Garden City is largely industrial with some trailer parks and aging housing.
Probably the closest fit to what you describe is the north and east ends. For easy access to the parks, fish & game and the greenbelt, your first choice would be the east end (or northeast Boise), focusing on the historic area around Walnut and East State. When you look at a map, you'll notice that there are a number of streets that form a grid in that area--that is the historic east end. Walnut leads directly to fish and game and the greenbelt. North of that area is Foothills East, a great foothills neighborhood. To the east there is a cute mid-century neighborhood (Louisa, Hot Springs, Hillview, Bacon) that is very popular.
The north end would also likely be a great fit for you and it might be easier to find housing there (though still a challenge as our rental and housing markets are very active right now). The area around the Boise Co-Op at 8th & Fort is very walkable with easy access to downtown, the foothills and not too far from the Greenbelt.
I personally live in the Central Rim area which I love because Garden Street north connects to the greenbelt so we're a 10 minute bike ride to the heart of downtown and also have great access to the rest of Boise. It's a fairly small neighborhood that doesn't have a ton of housing activity, but things come up from time to time so it's a good area to watch. Same with the Depot Bench and Morris Hill neigbhorhoods.
Hope that helps. I'm sure others will have thoughts to add. Good luck to you!