The [Time and Weather page][1] from the Ushi No Tane website's Song of Seasons guide says that the game will force you to go to bed at 05:59. This implies that like most Harvest Moon games you won't wake up any earlier than 06:00 when you go to bed for the day because you'll just to sleep again at 05:59. Since 06:00 is the normal wake up time, going to bed early won't result in you getting up any earlier.

The [Health and Stamina page][2] from the same guide lists the following benefits from going to bed.

 - +30 (out of 100) increase in health 
 - +50 (out of 100) increase in stamina
 - an additional +6 increase in stamina per hour slept

And the following penalty for going to bed late:

 - -5 to -30 penalty to health for going to bed after midnight. You'll also probably wake up later than 06:00.

This means you'll gain the maximum possible benefit from going to bed at 21:00, but only if you're at exactly 1 stamina. In that case you'll gain +30 health and +99 stamina. Since your maximum stamina is 100 (and this can't be increased in this game), if you're at 2 to 7 stamina then you'll get to this maximum by going to bed at 22:00 or earlier. If you have 8 to 13 stamina you'll only need to be in bed before 23:00. At 14 or higher stamina midnight is the cut off since that's when the health penalties start applying.

Unfortunately the game doesn't show you your exact stamina level. Having a  level of half a heart means you have 1 to 10 stamina points, a full heart 11-20 points, one and half hearts 21-30 and so on. Because of this I would set the earliest "optimal" bed time at 22:00. It's not worth to going to bed an hour earlier just for the unlikely chance you'll get one more stamina point.

If your stamina level is at one full heart or over, then the optimal thing to do is probably to spend it on useful stamina consuming activities until you're down to half a heart. The worst case cost of a single action appears to be 10 stamina, so you're never at risk of collapsing unless you're at half a heart. 

As for other things to do when you're down to half heart and don't want to risk passing out, you really shouldn't have that much trouble finding things do that don't cost stamina. I haven't gotten far in the game yet, and I'm guessing you haven't either, but here are some activities you should be able to do to fill up your time:

  - Talk to villagers. At least with marriage candidates simply talking to them once a day will raise their friendship level. I assume this should work with normal villagers as well. You also might learn something by talking to them, a hint about playing the game or what sort of gifts they might like.
  - Foraging. At the start most of the game world seems to be blocked off, but you can still find stuff lying on the ground like weeds, pebbles and honeycomb that you can pick up. Even if you can't find a use for them now, you might later. You can also catch insects, or befriending the animals.
  - Cooking. I haven't unlocked this yet, but I assume it doesn't take stamina like most Harvest Moon games. Once obvious benefit from cooking is that you can eat whatever you prepared and regain stamina. Even if you don't want to do that, you can often make something that ships for a higher price than the ingredients, or maybe even makes for a better gift for that special someone.
  - Go to town. Stock up on supplies you might need in the future. In particular it's good idea to get seeds in advance since you can't always depend on the stores being open on days when you want to replant. You can also visit the restaurant and have something to eat in order to regain stamina. If you're feeling really rich you can go to the doctor and pay your way to full stamina and health.
  - Visit the toilet or bathroom, sit in the hot springs, or take a nap. These all restore stamina, but you'll need to unlock them first.

Since the game uses the 24 hour clock, the times given in the answer are also in that format.

  [1]: http://fogu.com/sos1/basics/time-and-weather.php
  [2]: http://fogu.com/sos1/basics/stamina-and-health.php