The absolute pinnacle would be 4th and a cup.
More likely he'll have them in 5th-7th place, which actually would be an achievement because if Kane is cooked/disinterested then this is a team with 8th-10th place talent.
The biggest problem at Spurs for the last three seasons has been the squad, not the manager. Conte is great but he isn't a miracle worker. Going back to Poch's last 8 months in charge, three successive managers, none of them total slouches and four if you want to include Mason, have failed to get much of a tune out of players like Dele, Dier, Sanchez, N'Dombele, Lo Celso, Winks, and Bergwijn. All those guys are in their prime ages of 24-27 and are supposed to be the core of their rebuilding project. Any truly high end outcome for Conte depends on him whipping 4-5 guys from that group into shape. But the much more likely scenario is that they're just not very good, Conte will discover that eventually in the same way that Poch, Mourinho, and Nuno did, and he'll then end up telling Levy that the squad needs huge investment and overhaul to be competitive.