Puzzle Quest Galactrix

You need 13,230 Intel to get to level 50. About halfway through the story (Rites of Passage quest, found at Quesada Prime), you’ll gain the ability to play a “rumor” minigame, with fairly high Intel rewards. Below is a list of all 50 rumor locations listed in order of Intel given, followed by number of turns the game lasts. Find a difficulty that works for you. This is the most efficient way to level up, not many sidequests even go up to 50 intel points!

25 - 5 - Elea Tau (Elea)
25 - 5 - Krystallus Lambda (Krystallus)
25 - 5 - Medusa Alpha (Medusa)
25 - 5 - New Europa (Orion)
25 - 5 - Quaris Epsilon (Quaris)
25 - 5 - Quesada Tau (Quesada)
50 - 10 - Elysia Lambda (Elysia)
50 - 10 - Icarus Alpha (Icarus)
50 - 10 - Indus Delta (Indus)
50 - 10 - Megreb Theta (Megreb)
50 - 10 - New Aztekia (Ramses)
50 - 10 - Pleione Rho (Pleione)
50 - 10 - Sargon Pi (Sargon)
50 - 10 - Typhon Rho (Typhon)
50 - 10 - Vela Epsilon (Vela)
100 - 15 - Aries Sigma (Aries)
100 - 15 - Corvus Lambda (Corvus)
100 - 15 - Gemini Labs (Gemini)
100 - 15 - Keck Sigma (Keck)
100 - 15 - Krystallus Delta (Krystallus)
100 - 15 - Lacerta Omega (Lacerta)
100 - 15 - Leo Epsilon (Leo)
100 - 15 - New Antarctika (Alpha Centauri)
100 - 15 - New Ethipoia (Polaris)
100 - 15 - Plasmia Theta (Plasmia)
100 - 15 - Scorpio Theta (Scorpio)
100 - 15 - Zaurak Omega (Zaurak)
250 - 20 - Atlia Sigma (Atlia)
250 - 20 - Carinox Gamma (Carinox)
250 - 20 - Cradle of Quesada (Theseus)
250 - 20 - Fornax Epsilon (Fornax)
250 - 20 - Krystallus Iota (Krystallus)
250 - 20 - Leo Omicron (Leo)
250 - 20 - New Amerika (Aquila)
250 - 20 - New Asia (Lupus)
250 - 20 - Perseus Sigma (Perseus)
250 - 20 - Procyon Epsilon (Procyon)
250 - 20 - Sagitta Theta (Sagitta)
250 - 20 - Typhon Delta (Typhon)
500 - 25 - Electra Zeta (Electra)
500 - 25 - Eridanus Omicron (Eridanus)
500 - 25 - Gehenna Omega (Gehenna)
500 - 25 - Gomorrah Phi (Gomarrah)
500 - 25 - Krystallus Kappa (Krystallus)
500 - 25 - Leo Delta (Leo)
500 - 25 - Musca Epsilon (Musca)
500 - 25 - New Australis (Beta Centauri)
500 - 25 - Solis Mines (Solis)
1000 - 30 - Circinus Pi (Circinus)
1000 - 30 - Nashira Lambda (Nashira)

Another option is quick battles if you get tired of rumors and running around. I used the following skills:

-Data Synapse (turns purple gems into Intel points)
-Photonic Transformer (turns chosen color of gems to white)
-Multiphase Thruster (destroys one color of your choice - white, naturally)

With this set-up, one can farm Intel/experience fairly easily. it doesn't matter if you win or not since you keep your points either way. I averaged about 100 intel per battle though I did hit as high as 170.

I'm sure this could be improved with higher-level ships; I was using a Light Cruiser.

Once you have obtained the character Elgara to unlock Rumors just search for the Rumors in each system. Most of them are located on the moon areas. The minigame takes about the same amount of time as hacking a gate and I failed it less. It provides you with up to 500 Intel experience. When I hit level 50 my intel was 13,249 so I levelled up almost every time I found a Rumor.

I discovered Rumors very late in the game so I wound up only finding 17. I believe there are 50 total.

Other than Rumors the quests are worth the most experience points. You can have up to 4 quests at one time. I did all but a couple of these.