If you want to go for absolutely the most like OTL outcome possible, Henry Knox, Washington's friend and second-in-command, is elected to be the first president. The only difference is that Knox might serve a third term, or even a fourth if he's up for it (the old general died in 1806 in OTL), creating a much longer precedent. The capital might get named Washington anyway (in honor of the man still regarded as the Father of the US), but if you want to go for even more divergence the capital could be Knox, DC.
After M. Knox's third term ends, the 1800 election will be up in the air. Probably a Federalist would win (John Adams?) because the Democratic-Republicans will not have quite as powerful a base (being in the opposition during the Quasi War and Alien and Sedition crises really helped their cause, which won't happen to the same extent ITTL), but I think in 1804 it would swing to the D-R under Jefferson or possibly Madison / Burr. The navy would probably be larger ITTL, creating an interesting situation in the Barbary wars and beyond. I might have to revisit this idea, actually. It is intriguing.