Luhman 16 A&B - 6.5 LY
WISE 0855–0714 - 7.2 LY
WISE 1506+7027 - 11.1 LY
(Epsilon) Indi A&B - 12 LY
There will likely be more found closer as time goes by.
From WIKI
Common Name Scientific Name Distance (light years) Apparent Magnitude Absolute Magnitude Spectral Type
Sun - -26.72 4.8 G2V
Proxima Centauri V645 Cen 4.2 11.05 (var.) 15.5 M5.5Vc
Rigil Kentaurus Alpha Cen A 4.3 -0.01 4.4 G2V
Alpha Cen B 4.3 1.33 5.7 K1V
Barnard’s Star 6.0 9.54 13.2 M3.8V
Wolf 359 CN Leo 7.7 13.53 (var.) 16.7 M5.8Vc
BD +36 2147 8.2 7.50 10.5 M2.1Vc
Luyten 726-8A UV Cet A 8.4 12.52 (var.) 15.5 M5.6Vc
Luyten 726-8B UV Cet B 8.4 13.02 (var.) 16.0 M5.6Vc
Sirius A Alpha CMa A 8.6 -1.46 1.4 A1Vm
Sirius B Alpha CMa B 8.6 8.3 11.2 DA
Ross 154 9.4 10.45 13.1 M3.6Vc
Ross 248 10.4 12.29 14.8 M4.9Vc
Epsilon Eri 10.8 3.73 6.1 K2Vc
Ross 128 10.9 11.10 13.5 M4.1V
61 Cyg A (V1803 Cyg) 11.1 5.2 (var.) 7.6 K3.5Vc
61 Cyg B 11.1 6.03 8.4 K4.7Vc
Epsilon Ind 11.2 4.68 7.0 K3Vc
BD +43 44 A 11.2 8.08 10.4 M1.3Vc
BD +43 44 B 11.2 11.06 13.4 M3.8Vc
Luyten 789-6 11.2 12.18 14.5
Procyon A Alpha CMi A 11.4 0.38 2.6 F5IV-V
Procyon B Alpha CMi B 11.4 10.7 13.0 DF
BD +59 1915 A 11.6 8.90 11.2 M3.0V
BD +59 1915 B 11.6 9.69 11.9 M3.5V
CoD -36 15693 11.7 7.35 9.6 M1.3Vc