I would recommend Hunter in the morning and Slide in the afternoon to maximize the direction of light at the views.
The best approach (from a knee perspective) for Hunter is the Spruceton Trail (6.8 miles round trip) on a relatively easy old road trail. There is a nice western view at the Robb lean-to site (burned down from a camping accident). The view from the Hunter fire tower is among the best in the Catskills. The generally accepted high point on Hunter is a step up rock in the southwest corner of the fire tower clearing - near the Spruceton trail. There is an arrow pointing north carved into the rock. The Spruceton Trail approach will enable the shortest driving distance to a Slide Mountain trailhead on CR 47, south of Winnisook Lake. The very end of the Spruceton Valley Road is a little slow going - as the road is narrow and a bit rough.
It does seem that many hikers who climb both Hunter and Slide in one day prefer to climb Hunter via the Becker Hollow Trail. While it is the shortest (5.8 mile round trip), it is also the steepest and hardest descent for knees. Another approach is the Devil's Path trailhead at Notch Lake (7.5 mile round trip). Descending the Devil's Path is a bit easier than Becker, but either will take a toll on your knees. There is a parking fee for the Notch Lake trailhead while the Devil's Tombstone campsite is open (it closes Labor Day). The fee must be paid by stopping at the campground. Finding the ranger might slow you down a bit. All of the other trailheads have free parking year round. Either of the two eastern approaches from Route 214 will enable you to take in an excellent viewpoint over the Spruceton Valley -- it is on an unmarked path opposite the top of the Becker Hollow Trail.
To climb both mountains in a day you will want to do Slide Mt from County Route 47, south of Winnisook Lake. The stream crossing near the start of the hike can be difficult in times of high water, but most of the year it poses no problem. The shortest round trip to the Slide Mt summit is 5.6 miles. There is an excellent northern viewpoint just prior to the summit, and another eastern view (becoming overgrown) just past the summit from a rock ledge bearing the Burroughs Plaque (on the eastern/downhill side). If you have sufficient time, a descent on the Curtis-Ormsbee Trail is recommended. The trail junction is 0.8 miles west of the Slide Mt summit. This will add a mere 1.2 miles to the hike (6.8 miles total round trip), and it is an easier descent for the knees. On this route there are two excellent southern viewpoints on short unmarked side paths.
