Short answer - no.
San Lorenzo Market is in Piazza del Mercato which is several blocks north of the Medici Chapel, which is on the far side of Piazza del Duomo. Il Duomo is several blocks north of the river and Ponte Vecchio. It's within walking distance but it would be a long walk.
"near" is such a relative term...the mercato is 1.1 kilometers away from the bridge on foot, so about 15 minutes' walk...however, the entire way is through the pedestrian areas of central Florence, so it's a pleasant walk that has plenty to see on the way..so are they "near"? Well, the mercato is across the city center from the bridge...but the city center isn't that big...
P.S. it's "Ponte Vecchio"...
Yes, 15 minutes walking is about right. Although the route is mostly pedestrianised it is quite possible that you will be slowed up by other people: central historical Florence can be very busy indeed.
There isn't a simple public transport option from San Lorenzo to Ponte Vecchio. Central historical Florence is compact and very walkable, with only a few (small, electric) buses running through it. You can find their details here:
I would agree with the others that while it doesn't look exactly "near" on a map, central Florence is very compact so it's not at all far either. We didn't feel the need to use any sort of public transport during our last 5-day stay in the city.
Walking is the best way between both, and it'll be enjoyable one with much to look at along the way!
It is in my opinion a really nice walk away. As a mater of fact it is one of the worlds most amazing walks away. If you just walk flat out it is less than 15 min. I recommend that you take some time because it is an amazing stroll.
There are some nice restaurants and shops around the San Lorenzo Market. So it is good to take a little time and explore the area. Like the best Biscotti shop in Florence.
Have a Great Time,
What most of the others have said. My wife and I were there for only 1 day last May and we walked around most of the day except when we did board a bus just to quickly see a little bit more of the city, but even the bus we took did a circular route around the city and covered probably only a couple of miles.
As someone said near and far are relative terms. I would say the distance between the two was near and if you walked straight from one to the other with my long legs and fast gait I could probably get there in less then 10 minutes.