Есть = to eat : я ем, ты ешь, он/она ест, мы едИм, вы едИте, они едЯт (capital letters mark the stressed vowels)
Ехать = to be going on a vehicle or to slide: я Еду, ты Едешь, он/она/оно Едет, мы Едем, вы Едете, они Едут.
Don't confuse the verb Еду (I'm going) with едУ - the accusative case of the noun еда (=food). Ex. Когда я куда-то Еду, я всегда беру с собой едУ.
Lucas, technically, it should be "I am going" here. "Я еду" means going right now or in the nearest future - this is what continous (progressive) tenses are for. English is not my native language, so I can't be 100% sure native speakers don't use Present Simple instead of Present Continuous, but to me, it just does not look right.
"I go" is usually used when you talk of some regularity. I go to Saint Petersburg every week. In Russian, that would be "Я езжу в Санкт-Петербург каждую неделю".
You can say that if you are a hiker walking to St.Petersburg. Unlike “going”, which does not specify whether you are walking or going in a vehicle, «иду» only means “I am walking”. So, in this case, «Я иду» is a possible, although less likely than «Я еду» translation of “I am going”.
Your answer is fine, except Saint is usually abbreviated to St. The part Санкт was usually omitted before WWI. On August 18, 1914 according to Julian calendar ( i.e. Aug 31, 1914 according to Gregorian calendar), the city was renamed to Petrograd and 10 years later — to Leningrad. That name was in use until 1991 when the historical name was returned.