Ok, first any jobs can technically solo, but only a few can do it from the start to finish without much gear help. If your job isn't a solo friendly job… you will be stuck in the following "book burn" parties.

Solo Jobs: Dragoon / Beastmaster / Summoner / Thief,Monk,Warrior,Paladin,Dark Knight-main Dancer-subjob / Dancer / Samurai / Blue Mage / Ninja / Red Mage

Jobs to avoid as a Newbie: Puppetmaster, Corsair, Ranger (Each of these cost a TON of gil to maintain and just starting out you won't be able to finance it.)

Mage Jobs: White Mage, Black Mage, Scholar (Technically they can solo, but you won't have much fun doing it. Death is very common with these jobs on a newbie leveling up. Stick to parties, you will enjoy the game a lot more.)

No Abyssea - Abyssea will get you to 99 in literally hours, however if this is your first job or are underskilled, leveling in Abyssea will just give you a worthless character that is 99. Abyssea is meant for vets to level that extra job quickly, and not spend days doing it for something that is already skilled. If you are underskilled, your character acts just like he is the level that you are skilled for! So if your 99 with an evasion skill of 250, the first mob you go attack, will likely hand you your ass.

15-30 - Gusgen Mines - Entrance Pg. 1
35-60 Crawlers Nest - Entrance Pg. 1
60-75 Bostaunieux Oubliette - Sewers Pg. 4
75-99 Abyssea - La Theine - Worm Party

The above path is pretty much your go-to for speed leveling. Typically it can take 2-5 days to go from 1-99 depending on your job and playtime. Sticking only to this path, is boring as hell, and i'd recommend branching out and go solo in the following spots. Its also worth noting that if you don't at least solo some, you will completely neglect your skills and be worthless at 99. Here is your alternate spots… WARNING: Not very populated, so don't come here expecting parties.

Note: The following Levels tend to favor pet jobs, so if you are on another job, considering going to the next area at a later level.

1-10 Any of the starting areas

11-15 Any of the starting Crag area's.

15-29 Maze of Shakhrami
4 Maze Makers / 2 Combats @17+ Page 2
Starting with worms Maze makers. Worms can't chase but have a couple dmg dealing spells that can hurt. A form a silence makes the worms very trivial.

20-33 Korroloka Tunnel
2 Land Worms / 4 Seeker Bats @20+ Page 1
Fighting worms, the same strategy as Maze of shakrami.

25-29 Qufim Island
9 Clippers / 1 Land Worm @26+ Page 1
8 Clippers / 2 Seeker Bats @27+ Page 2
Worms untill 27~28, then bats from 27~29. Be sure to fight far far away from any undead at night due the blood aggro. Note: Bats have powerful evasion down move, and worms are casters.
The FoV can be used in conjunction with this camp and the exp is great. Though it lacks a page which targets the worms or bats to a high degree and makes the clippers and pugils the main focus. Clippers were harder fights to close as they stack up the defense but are manageable. The pugils can be slightly tougher. By using the pages and then filling in the space between acquiring pages with worms and bats the exp is great.

28-32 Lower Delkfutt's Tower
3 Bats / 3 Gigas @ 28+ Page 2
Gigas have horrible acc and eva, so hitting them is no problem, and once you're 30+ you can very well kill either of the NM Hippolytos or Epialtes that spawns on the second floor. Drops Gigas Bracelets. I found this camp to be very enjoyable and fun and great exp.

32-37 Lufaise Meadows
No Fields of Valor Book Skilling / Scenery / Slow Exp
Lufaise Meadows Camp at the zone line to Tavnazian Safehold for the first few levels. If you link any bee's, the zone line is right there at the camp and you can simply zone to save your butt and your exp. Bee's are difficult targets to tank. Period. Pollen can restore a lot of their HP… A LOT. And their other TP move Final Sting WILL kill you if they use it at or around 50% or more of their health. Needless to say, this camp can really be a pain in the butt. But setting your Home Point in the safehold and changing jobs to restore HP rather then heal forever will get you those levels soon enough, probably faster then looking for a party will. Kill sheep as soon as they start checking even match, or try them as tough.

32-39 Eastern Altepa Desert
10 Giant Spiders @ 32+ Page 1
Sickle Slash is alot like Final Sting in that it can completely waste your characters HP instantly.

39-43 Riverne - Site A01
No Fields of Valor Book Skilling / Scenery / Slow Exp
Hawkertraps will be what you are killing here. Only bad TP move, is there AE Paralyze.

35-45 Upper Delkfutt's Tower
6 Gigas @ 35+ Page 1
Love this camp, and its nice seeing gil drop from every mob. This can be revisited at 70+ for the top 2 levels.

45-47 Yhoator Jungle
10 Young Opo-opos @ 45+ Page 3
7 Worker Crawlers / 3 Young Opo-opos @ 47+ Page 4
Worker Crawlers and Young Opo-opos in Yhoator Jungle. Around Outpost for Opo-opos and Tunnels for Crawlers

47-57 Crawler's Nest
3 Bees / 3 Crawlers @ 47+ Page 1
Entrance Bee's and Crawler's

55-60 Western Altepa Desert
2 Goblin / 8 Tulwar Scorpions @55+ Page 4
Goblins in Western Altepa Desert. They are in the South West corner around a lake.

60-65 Newton Movalpolos
No Fields of Valor Book Skilling / Scenery / Slow Exp
Watchout for Black Mage Goblins, Shadows/Blink Recommended. Not really the best camp, but if your itching for a change in scenery give it a shot.

65-99 Ro'Maeve
3 Killing Weapons / 3 Ominous Weapons @ 65+ Page 1
7 Cursed Puppets @ 70+ Page 3
Around Entrance

75-99 Ru'Aun Gardens
5 Flamingos / 3 Sprinklers @ 75 Page 1
11 Groundskeepers @ 80+ Page 3
Entire Zone filled with them

85-99 Gusgen Mines
2 Accursed Soilders / 5 Rockmills @85+ Page 7
(F-8) Map 2 is a room filled with Rockmills which are worms you can skill up on, magic users should use this to max out all the offensive spell casting. Accursed Soldiers you have to hunt down in the hallways, and only 8 spawns in the entire zone. Not the most efficient book burn, but great for skilling up and getting exp as well.

92-99 Garlaige Citadel
4 Fortalice Bats/ 3 Warden Beetles @ 92+ Page 8
The basement area (first hole dropdown as you enter zone) your targets are bats and beetles and as a bonus GoV was recently add by the stairs as you enter the basment area the bats and beetles do not agro and only the beetles will link, Just becareful of the bombs as they still agro like usual and finally don't forget Reraise III from the book!

99/Merits/Skills Gustav Tunnel
5 Boulder Eaters / 2 Pygmytoises @ 99 Page 8
Located in the depths of Gustav and once again SE was kind enough to provide a page fitting for this area your target are the giant worm and tiny turtles and with page 8 capping at 4630 EXP you can easy achieve 40k an hour and also don't forget bringing a healer or dd with dnc sub is also useful for getting those final skill ups on range and melee.