7:43 p.m. on January 14, 2013 (EST)
San Jacinto 10,800', could have some late snow but by May things should be very pleasant even if fairly wet. You shouldn't need crampons, but it might get into the 20f's at night. If not camping near the summit, you might consider Round Valley. http://www.msjnha.org/park/camping.html
A trip up the tram would be a quick way up and would more likely kick in any severe altitude problems within 24 hours. Those most susceptible notice problems over 8,000'.
The trick with Whitney is a day trip. You are up and down before the devil altitude knows you have been there. Most problems show up overnight at Trail Camp. You can expect routine acclimatization problems of lassitude, a bit of light nausea or loss of appetite, a headache and sleeplessness (an apnea induced by altitude). Most of the headaches go away with Ibuprofen the remainder will go away as you return to lower altitudes. More than likely you will not have any significant altitude induced problems. Being very sick up there is a very rare occurrence.
If you follow the usual route and stay at Trail Camp (12,000'), you can usually get up to the top the next day and return and feel only minimal altitude affects. About what you would feel overnight on San Gorgonio just north of San Jacinto.
San Gorgonio ( http://www.sgwa.org/Wilderness_Mileage.pdf) at 11,500' is closer to the highest overnight altitude you might be on Whitney - unless you stay at Consolation Lake. Gorgonio is bit higher than San Jacinto and would give you a more of a challenge and closer comparison to the effort getting up Whitney. This would be especially true if you went up from the South side at Vivian Creek camping at High Creek 9,400' (Whitney Portal elevation about) or even on the saddle overnight. We've dropped packs in early afternoon and made the summit and back for the night at High Creek. I've spent the night just off from the summit a few times. Nice sunrise.
In either case get your wilderness permit early on. And check in a few days before to find out weather conditions at your chosen campsites and summit.
Mt Baldy as a day trip and even the Three T's AND Baldy as a day trip would test your fitness. Another test would be up and down Baldy in the morning have a lunch and then do it again in the afternoon. Good hamburgers at Mt Baldy Village Restaurant. Also nice fireplace.
Performance at altitude and the degree of physical fitness have very little in common, other than you can get higher faster if fit and thereby have a chance of getting sicker faster.
True acclimatization at 12,000' takes over a month, with a lot of gain in the first 6 days. Full acclimatization at 14,000' takes a bit over a year. So in affect almost nobody is acclimated for that altitude in a week or so.
The usual place most like to stop at for an altitude check is 10,500' drive to camp from Lone Pine, at Horseshoe Meadows. I prefer to let the altitude catch up to me on the trail, taking it slower, and get a good night sleep at a much lower altitude.
A nice local quick hump of a trail is up from Chantry Flats (north on Santa Anita east of Pasadena on I-210). Go up Mt Wilson using the trail going past Sturdevant Camp (ends on east side of mountain near the big array) and then down from the trail in the main parking lot and taking the ridge route that connects to Upper Winter Creek trail back to your car. A pleasant 14 mile day trip that you should be able to coast on if doing Whitney.
If you miss your permit on Whitney from the east side, consider the west side from Horseshoe Meadows over Army Pass catching Mt Langley on the way down Rock Creek then up to Crabtree Meadows and Guitar Lake dropping packs for a day run on Whitney. Return with a car shuttle over either Forester Pass and up to Kearsarge Pass and Onion Valley, or cut it short by going over Shepherd Pass picking up Mt. Tyndall on your way down the pass. If you capture Mt Muir on the way back from Whitney, that would be a four billiard cushion summit trip.
Although strenuous you would see a lot of the best in the Sierra in one trip.