Multiclassing
For completeness, we'll get the obvious ones out of the way first. A level into Barbarian, Monk, or Draconic Sorcerer will get you an unarmored base AC of 10 + Dex + Con, 10 + Dex + Wis, or 13 + Dex respectively.
Races
There's obviously the Tortle which will set your AC to 17, but also Lizardfolk for a 13 + Dex AC that technically also works with armour (not that it's relevant here) and Autognomes and Thri-Kreen get the same but which only works without. Loxodon get the perhaps more interesting 12 + Con unarmoured AC. Otherwise it's worth noting that Warforged +1 to AC does not require you to wear armour. Similarly the Simic Hybrid's +1 (choosable at 5th level) works which anything other than heavy armour.
Or as final alternative, being a Dragonborn and picking up the Dragon Hide feat is another way to get 13 + Dex.
Spells
There are also three spells of real note to AC. Barkskin will set your AC to 16 for up to an hour, though since it's 2nd level and requires concentration it's not great for casting on yourself. Shield of faith is a first level spell which gives +2 to AC, but which the same concentration problem and only lasts up to 10 minutes.
Far more relevant would be mage armour, which gives 13 + Dex, lasts for 8 hours, and can be gotten with the Magic initiate feat or with Eldtrich Adept if you'd rather have at will casting over two cantrips.
Feats
Beyond those feats relevant to options above, the Duel Wielder feat comes with a +1 to AC, admittedly that's while wielding a weapon in each hand, which rather goes against your general plan.
Temporary bonuses
That covers the player options for buffing your AC over the longer term, but there's a few others that are relevant to mention at least.
- The Evasive footwork Battle Master maneuver lets you roll a Superiority die and add it to your AC while moving.
- Defensive Duelist lets you add your proficiency to it for an attack, though while wielding a finesse weapon you're proficient with
- War Magic wizards have a similar feature
- Shield gives you +5 until the start of your turn
- and haste gives +2 for the duration
- Bladesingers add their Intelligence to AC while their Bladesong is active
Magic items
Magic items become something of an infinite well, and of course aren't generally available as a player option, but the cloak and ring of protection will increase any AC and Bracers of defense increases unarmoured AC specifically. The cloak is replicatable by a 10 level Artificer, and the ring and bracers by a 14th level one.
And of course there's items that can only be obtained through the good will of the DM or adventure writer, such as Defender, Ioun Stone of Protection, Badge of the Watch, or Flying Chariot.