Highest Level a character can reach with CR2 encounters

[Jack Simth]

According to this calculator, level 10. You'd get 225 XP per CR 2 encounter at level 9, and keep doing so until you level up. At level 10, you get 0 XP per encounter.

That calculator is based on the table in the DMG - page 38 (it's not in the SRD). As long as the challenge is withing seven levels of the character, the character gets XP (in differing quantities) as listed on the table - hence, a level 1 character that solo's CR 2 encounters indefinitely would stop getting the listed XP for them at level 10.

However, that calculator is missing the two footnotes that show up on the actual table:

The table doesn’t support XP for monsters that individually are eight Challenge Ratings lower than the character’s level, since an encounter with multiple weak creatures is hard to measure. See Assigning Ad Hoc XP Awards, page 39

and

The table doesn’t support awards for encounters eight or more Challenge Ratings higher than the character’s level. If the party is taking on challenges that far above their level, something strange is going on, and the DM needs to think carefully about the awards rather than just taking them off a table. See Assigning Ad Hoc XP Awards, page 39.

Due to ad-hoc XP awards, per RAW the answer is "as high as the DM says" unless you add further restrictions (such as "only one CR 2 critter at a time").

Don't forget about the boredom factor. Based on my quick calculation, a single 9th level character would have to go through 40 CR 2 creatures to get to level 10. A party of four would have to go through 160. At some point the player's are going to throw up their hands and bring the whole dungeon down rather than go through more boring CR2 battles.

However, at those levels, you very well can build a character that can take on those 40 CR 2 critters sequentially in relative safety - without resting, even. Say... with a Ring of Invisibility and the Summon Elemental Reserve Feat (Complete Mage - the right Wizard build can obtain it at 7th, most builds will wait until 9th) the majority of CR-2 encounters simply can't oppose the Wizard at all anymore.