We have an "overland" GMT 800 suburban that's mostly a highway cruiser in between daily driving. A few handling upgrades have made quite a difference in the handling. I found a used Hotchkis performance suspension system that made it pretty sporty- included new f&r sway bars and bushings and new rear lower control arms. The rear control arms are way beefier than the stamped factory pieces. Of course the stiff rear sway bar made the ride harsh on anything besides smooth pavement, so I found some Eibach sport lowering springs (think same as PPV Tahoe rear coils) and put the factory sway bar back in. Almost the same level of handling, but none of the harshness when a tire hits a pothole, etc. Bilsteins all around to freshen up the shocks. Even with the suburban sitting somewhat low, we've done a couple forest service trails that have impressed me. It helps having the G80 rear locker, which hasn't blown up on us yet. I picked up a set of the Moog replacement coils for under $50 for a 2500 Mile road trip hauling a horse trailer. Though it sits 3" higher in the rear with these springs, they keep the burb handling pretty well with the added spring rate and are pretty easy to swap when needed.
It ain't glorious, but our boring 03 burb has taken us lots of places. Get some good monotube shocks, some firmer rear coils (the lower the better for handling, depends how loaded you usually are), and upgrade the sway bar bushings to polyurethane. Spohn makes good replacement rear control arms, too. Won't be a Corvette, but you'll notice a difference.