I swear I've seen it in the Monster Manual, but I can't seem to find it anymore. Where can I find statistics for dragonborn and half elf NPCs?
As far as I'm aware, the only mention in the Monster Manual of NPCs with a specific race is the following:
Racial Traits. You can add racial traits to an NPC. For example, a halfling priest might have a speed of 25 feet and the Lucky trait. Adding racial traits to an NPC doesn’t alter its challenge rating. For more on racial traits, see the Player’s Handbook or the D&D player’s basic rules.
So basically, if you want a dragonborn NPC, you should give them a breath weapon and damage resistance, just like a dragonborn PC. For half-elves, you would give them Fey Ancestry, Darkvision, and 2 skill proficiencies. Obviously in both cases you would also describe them with an appearance appropriate to their race.
You might have been thinking of half-dragon NPCs rather than dragonborn - half-dragons have a very well defined template which you add to an NPC to make it a half-dragon. (It's under H for half-dragon.) I'm not sure what you could have been thinking of for half-elves, though.
You should check out the Dungeon Masters Guide. On page 282 it explains the creation of NPC's from scratch. It has a list of Racial features the NPC could have.
Dragonborn* +2 Str, + 1 Cha Breath Weapon (use challenge rating instead of level to determine damage), Damage Resistance, Draconic Ancestry; speaks Common and Draconic
*See the Player 's Handbook for descriptions of this race's features , none of which alter the NPC's challenge rating.
Another place to look is Appendix B from the Monster Manual (page 342), It contains stat blocks of "Medium humanoid (any race), any alignment"