The Bladesinger can consistently do this (depending on Short Rest application)but it has limited uses per adventuring day
This answer is a little problematic due to game pacing and DM discretion on whether or not a short rest happens in a given game "as designed" (two short rests per long rest, per DMG) - the bladesong class feature is usable twice per short rest. For DM's or scenarios where short rests don't happen, this goes out the window and can only be done twice ... in the original version of Bladesinger(Sword Coast Adventurers Guide). In the Tasha's Cauldron of Everything version, you get "proficiency bonus uses per long rest" which means that the number of uses is tied to the PCs level. With that caveat...
For practical purposes, AC is needed when combat arises, and the bladesong will usually be activated in a combat situation. The Mage Armor, once cast, lasts for 8 hours so the walking around AC will be Dex bonus + 3 (16-18) while combat AC will get this enhancement.
Bladesong, at level two, adds the Int ability modifier to AC.
While your Bladesong is active ... you gain a bonus to your AC equal to your Intelligence modifier (minimum of +1). (Sword Coast Adventurer's Guide)
An unarmored Bladesinger at level 2 w 16 Dex/ 16 Int, plus mage armor, gets AC of 19.
At level 4, AC of 20
At level 8, AC of 21
At level 16: AC of 23
Assumption: all ASI's are assigned to Dexterity and/ or Intelligence, and the PC uses either point buy or standard array to start with 16 Int and 16 Dex. (For rolled stats, the elf or half-elfPC may start with slightly higher stats, so the AC would be higher a bit sooner).
If a single level of fighter is taken to multiclass, then taking the Defense fighting style adds one to the above numbers.