The strong inductive effect of two nitrogen atoms in histidine makes it more basic.

The bicyclic structure in the tryptophan side chain causes high steric hindrance making the nitrogen less basic.

The lone pair of electrons of the side chain nitrogen in tryptophan is part of aromatic conjugation which is why it is not available for protonation while the lone pair of one of the nitrogen of histidine side chain is available for protonation making it more basic.

The five-membered ring in the histidine side chain causes high ring strain making the nitrogen more basic.