With the current fitness leveling, here are the optimal runs so you don't get too much fitness experience (excess experience is dropped since the value is reset; it may be intended by Salia so players don't powerlevel it early on and have to wait a minimum of 10 days to cap - which already is nicely challenging)
You level up overnight and can only level once a day. May be subject to change at any time but as of the current version:
Sprinting XP: 20, Running XP: 8, Jogging XP: 2, Walking XP: 0. Walking twice in a row initially disqualifies the player; walking twice in a row at most after any non-walking action is fine. (You'll still get the XP either way, but won't get the reputation or energy recovery from finishing.)
The optimal use of jogging/running/sprinting is based on your max energy at the time as well as the energy costs for the current level.
Strawberry milkshakes can push you to 150 and some events also grant additional max energy. You don't need the reputation for now and you can farm it later, so just play lazy and lay on the ground (sacrificing some current willpower in the process), remember to also use any fresh item immediately.
Base energy costs at Level 0: 100 for sprinting, 50 for running, 10 for jogging
Level 1: 10 XP; 98/45/9 and +5 Max Energy (can be easily done in 5 jogs on day 2)
Level 2: 25 XP; 95/40/8 and +6 Max Energy (can be easily done in 13 jogs on day 3)
Level 3: 45 XP; 90/35/7 and +7 Max Energy (that's 23 jogs now costing 161 energy)
Level 4: 60 XP; 70/28/6 and +8 Max Energy (30 jogs costing 180 energy)
Level 5: 100 XP; 50/20/5 and +9 Max Energy (sprint 5 times or jog 50 times or run 12 times and jog twice, all options costing 250 energy)
Level 6: 160 XP; 35/15/4 and +10 Max Energy (sprinting is the most efficient at a cost of 280 energy for 8 sprints)
Level 7: 240 XP; 25/12/3 and +11 Max Energy (sprint 12 times at a cost of 300 energy)
Level 8: 350 XP; 20/8/2 and +12 Max Energy (sprinting or running alone would give too much XP so jog the rest at a cost of 350 energy)
Level 9: 500 XP; 17/6/1 and +20 Max Energy (jogging is the most efficient at 250 energy if you can take 250 jogs)
Level 10: 999 XP; 15/5/1 and +40 Max Energy (same as above, but jog 500 times)
Once you hit level 9 or 10 you can start farming reputation with jogs if your goal isn't to be done as soon as possible. Stand proudly after expending 10 energy and enjoy your 10 reputation. (If you already have a ton of energy at this point somehow, it's also what you should do unless of course you are after the scene.)
It's almost impossible to be done by day 11 (you cannot use the gym during tutorial day) but it's doable.You can do it at any point and ask her to stop harming your reputation once it's too late. The sooner the better at this point, but as long as you remember to go see her every 4 days, you're good. Once she agrees to stop harming your reputation, you can go back there at any time without consequences.Not going to lie, since you get energy in the process, time doesn't pass and willpower doesn't drop too much (max willpower doesn't drop either, fortunately), I absolutely love going "wew, this was exhausting" and refusing to stand up until I get hypoxia from being trampled. She's also very cute indeed and the extra verbal abuse is epic.