This advice is for Platinum's main singleplayer campaign. If you're playing DP or if you've already defeated Cynthia, you're on your own.
You can get an exp. share from Eterna City's south gate.
The best HM slaves are probably Bibarel (rock smash, cut, surf, strength, rock climb, waterfall) and Tropius (rock smash, cut, defog, fly, strength). You can use a Bidoof for rock smash and cut before you can catch a wild Bibarel. Evolving a Bibarel just for HMs isn't worth the experience.
Daily events reset when the clock advances from 23:59 to 00:00, so it's easy to abuse this mechanic if you're willing to mess with your device's clock.
Useful HMs, TMs, and held items and their locations
TM27 return: Sandgem Town (received upon leaving the lab), Lost Tower
TM26 earthquake: Wayward Cave 1F (accessed from B1F's southeast corner, requires bicycle)
TM31 brick break: Oreburgh Gate B1F (requires bicycle)
TM65 shadow claw: Hearthome City (received upon defeating Fantina)
TM38 fire blast: Veilstone Department Store
TM52 focus blast: Veilstone Department Store
Metronome: Veilstone Game Corner
TM13 ice beam: Veilstone Game Corner, Route 216 (requires rock climb)
TM29 psychic: Veilstone Game Corner, Route 211 east (requires rock climb)
TM75 swords dance: Veilstone Game Corner
TM89 U-turn: Veilstone Game Corner, Canalave City
If you want a Game Corner item, it's usually easier to save up regular money than to play the minigames. You can get an amulet coin from Amity Square.
TM28 dig: Maniac Cave
TM60 drain punch: Veilstone City (received upon defeating Maylene)
HM02 fly: Galactic Warehouse entrance
Ice punch, thunder punch, fire punch, dive, zen headbutt, sucker punch: Route 212 move tutor
Each of these moves cost at least 4 blue shards, so if you want to learn them, you'll probably want to pick up as many blue shards as possible. You can soft reset for any shard in the Great Marsh by saving right before entering.
TM30 shadow ball: Route 210 north
Choice specs: Celestic Town shop (morning)
HM03 surf: Celestic Town ruins (received upon defeating Cyrus)
TM19 giga drain: Route 209 (requires surf)
TM24 thunderbolt: Valley Windwords (requires surf)
TM84 poison jab: Route 212 south (requires surf)
TM35 flamethrower: Fuego Ironworks inside
TM81 X-scissor: Route 221
Expert belt: Route 221 level house (after receiving black belt)
You can soft reset for lower levels if you save before talking to the person. At this point in the game, you can buy both nest balls and quick balls, so catching low level Pokemon should be easy.
TM23 iron tail: Iron Island B2F east
TM91 flash cannon: Canalave City (received upon defeating Byron)
TM36 sludge bomb: Galactic HQ underpass
TM57 charge beam: Sunyshore City (received upon defeating Volkner)
HM07 waterfall: Sunyshore City (after defeating Volkner)
TM71 stone edge: Victory Road 2F
TM79 dark pulse: Victory Road 2F (northwest corner accessed from 1F)
