Though Mark Twain is interesting, I would suggest consideration of Elmira CC which is not far away. Two distinct nines. The opening nine is a Willie Dunn creation (a bit before the Golden Age) that is hilly and heavily wooded. The 1922 Tilly nine is down in the flats and out in the open. Interesting green sites on both sides. Would definitely choose Elmira over Corning.
I strongly disagree here Ed, and I think you've got the history wrong on Elmira.
What is now the front nine contains five holes (3-7) that were built in the late 1960s. They range from mediocre to downright horrendous. 3 is passable, but 4's green is unputtable, 5 is extremely awkward, 6 has a fairway that is too steep to hold, and 7 has a pond manufactured into a mountainside. Originally, the first six holes played up the mountain, with 3 and 4 being back-to-back par threes over gullies. Then, the current 10-18 played as 7-15, with a few alterations. 16 was a short par three to a tiny green (still visible today). 17 was a short par five playing downhill over the current parking lot and tennis courts. 18 was a par three back up the hill to the clubhouse. By all accounts (my great-grandfather and aunt were members there, and my dad played there many times as a kid), the original holes were a great deal of fun, and the current holes on the front nine are a poor substitute. My great-grandfather referred to the new 5th hole (the long par five up the hill" as the "A-Hole." What remains of the original course seems to be the least exciting of the original holes. To me, only 8 and 9 stand out as anywhere above average.
At the very least, holes 3-7 were added anew in the late 1960s (to ruin the golf course, apparently). In addition, greens were moved on holes 15 and 18. At most, Elmira C.C. has 11 original holes, and the new holes are all but unplayable. Maybe worth a look once as a painful reminder of how wrong a renovation of a classic course can go, but definitely not worth the trouble as a one-shot deal in the region.
For my money, Mark Twain is the fair superior golf course. The original routing and tremendous set of greens remain. You get two excellent par fives on the front nine at 3 and 5. All 4 par threes play uphill, and each one is very engaging. The course has some muscle, but it won't beat you up too badly because it lacks any overly penal hazards. Moreover, Mark Twain was built in 1937, late in Ross's career when golf course construction was scarce. Very interesting historically from my view. Did I mention it is dirt cheap to play?
Elmira C.C. and Mark Twain offer an interesting contrast. Elmira shows what can happen when an overzealous and undereducated membership loses respect for the history of its golf course. Mark Twain shows what can happen when nothing changes at a public course at all.
My recommendation: STRONGLY IN FAVOR of Mark Twain, and STRONGLY AGAINST Elmira C.C. If M.T. is unavailable that day, slip over and play Soaring Eagles. It has some fun, quirky holes, and it's also the home course of two PGA Tour pros (Joey Sindelar and Mike Hulbert). There is definitely good golf in the southern tier, but you won't find it at Elmira C.C.