I like the K-frame over the L-frame S&Ws (more handy, less weight, more pointable). Since carry isn't one of your criteria I'd strongly consider a 4" or 6" S&W K-frame .357mag (M19, M66, M13 or M65). I prefer the 3" (it handles better than just about anything I own or have shot), but if you don't think you'll ever CCW it the 4" gives most of the handling advantages of the 3" and it is much easier to find (and should be a little cheaper when you do find one) and the 6" may give some accuracy advantages due to the longer sight radius.
You may also want to consider the .357mag Taurus 66 or Taurus Tracker (both are basically K-frame size and hold 7 shots).
The big advantage of the .357mag is versatility- it does a little of everything. You can chamber .38spl so you can use very light target wadcutters, capable defensive .38+P JHP for home defense, good .357mag JHPs for home defense (though overpenetration may become an issue so I stay with .38+P for HD), to barn burning .357mag loads or heavy 180-200gr .357mag loads for the woods or just for fun.
If you would consider reloading, and since carry isn't an option, you also may want to consider the S&W 57 or 657. .41mag has become my favorite caliber, it is a ton of fun. It is more powerful than .357mag, it has less recoil (i.e. it is more managable) than .44mag, it can handle most dangerous animals you may encounter in N. America if a woods gun is a consideration, it is made on the same frame size as the S&W .44mag but is a smaller diameter so chamber and barrel walls are thicker so it may be a slightly stronger gun than the S&W .44mags, there is just too much going for it. However, ammo cost and availability are not strong points so this is really a reloaders caliber these days. The 57 and other S&W N-frames are just beautiful guns, and the older ones are outright works of art.
For something more utilitarian (maybe you may decide to carry it as a woods gun, or even occasional CCW), the Taurus Tracker is available in .41mag. It is K-frame size and weight so carry is easy. The ports and "ribber" grips make recoil somewhat managable (though I don't care what anyone says, until I experience it I assume it will still be something of a bear, a 34oz .41mag, it does sound fun though).