Nagelsmann was managing Leipzig before joining Bayern Munich as you know. Therefore I don't think Tottenham is much of a recession for him.
He wouldn't like to return to an average team again after this big step forward I guess. Tottenham would be another nice option to go for. Maybe Tottenham aren't a team that has a history full of titles. But still they are a really strong team now considering their players in the squad. Kane is their biggest card above all else. But Kane might also think of leaving also after having another season without a title. I don't know if Nagelsmann would be the manager to make Kane think twice about that.
Apart from Tottenham, who are rumored to be interested in Nagelsmann, there is also Spanish giant Real Madrid who made an approach with the former Bayern Munich coach. Real Madrid projected Nagelsmann as a replacement for Ancelotti, who is currently also rumored to be the new manager of the Brazilian national team. Nagelsmann was considered appropriate to replace Ancelotti because he was a young coach who had successfully brought Bayern Munich to several titles.
If these rumors are true, I believe Nagelsmann will choose Real Madrid over Tottenham, because given the great history that Real Madrid has made and Nagelsmann can continue this tradition. To train Real Madrid is not easy and is exactly like training Bayern Munich, because the club has big players who sometimes have their own egos, but Nagelsmann has managed to keep the Bayern Munich squad solid and maybe that is also a consideration for Real Madrid's management