earth is best place for public events, it has the most spawns of them and in 1 hour you can usually get 6 or so done with a little circle path. i usually will hit mothyards at :27 or :57, then head to divide at :10 or :40 for spider tank, i do as many of the little patrol quests (the green glowy things) as I can since they give 10-25 rep each, no cap on doing em. you can grind em out all day and hit vanguard rank 3 in a single day if you want, and get marks from public events (100 cap per week).
Destiny Public Events - Timer and Map
everything in game is solo'able except for the raid (and even that is soloable right now for large chunks of it) although obviously you need the gear. you can solo the 28 nightfall/weekly at around 26 or 27, but you need an icebreaker exotic weapon since you can always hide way back and snipe shit and IB regens ammo. to get to 28 fastest you'll wanna level vanguard fast by doing tiger strikes, bounties (rep), public events (for marks), and getting luck with engrams. you hit level 2, buy 2 of gloves/chest/boots for 120 marks (2 weeks), get hopefully some free shit at level 3, get one exotic item from xur either for motes or coins, and buy helm on week 3 for 120 marks (80 from second week carry plus 20 from third), upgrade them asap with shards, and blam you are level 28 or 29 now and can solo everything and do group raids.
the game plays vastly different at 28 than below, since you can solo so much stuff now especially nightfall which gives you a 20% rep boost bonus every week. at 28 the only thing left to do really is get the few unique items from the raids (ship, speeder, 4 armor pieces for your class, a couple of weapons) and then you are done. i've only done the raid a single clear and have like 80% of the items you can get from it, mostly from cheating and soloing atheon 2 weeks now.
pvp is also a great source of gear, since you get random shit at the end of every game, and just like vanguard you can buy gear at rank2 and for every faction you get free random gear packages every rank you hit at 3 and above.