If you go on a weekday, I'd pick Cascade but would avoid on a Saturday or Sunday due to the crowds. (It's Pierce or Jackson like)
On a weekend, I'd look at Wright or Phelps or Big Slide. (Big Slide provides some of the best views of Gothics.) Many people would tell you that you either have to stand on Gothics or see Gothics to get the best views of the ADK's. (Wrights may be similar to climbing North Twin or Carter Dome via Zeta Pass, a pretty easy beginning that then does some climbing, Big Slide depending on approach, Garfield liek but with many more views down low when going over the Brothers)
Algonquin is worthwhile to add to a trip to Wright's but may push you past moderate. Parking for Big Slide at the garden can be problematic, full most weekends & Fridays, requiring a shuttle ride.
I'd look at a long weekend & I'd opt for a couple. It would be like trying to give an ADK climber one peak they should climb in NH. (Garfield or Carrigain would be on my short list but you'd need Franconia Ridge & a Presidential or two.)