Auxerre is located half way between Paris (170 km) and Dijon (150 km) on the A6 motorway, at the junction of the proposed A26 Troyes-Bourges motorway. The city is ideally situated to discover northern Burgundy.
Trains are a wonderfully cheap option if you are coming from Paris or Dijon. Trains usually run every hour. If you are coming from Paris, you might have to make a connection at Larroche-Migennes. You can easily walk from the station to the old part of town in 10 minutes.
Auxerre is small in area, so walking is highly recommended for most purposes and is a pleasant thing to do in the old city.
There are free mini buses that circle the periphery of the old town as well as a bus system that services suburbs (for the suburb bus, tickets are 1 euro 75).
Walk across the pedestrian bridge that spans the river as it gives a nice postcard view of the city. Rent a bike at the train station and bike south along the Yonne river towards a charming town called Vaux. Rent a kayak and paddle around the river next to the Parc des arbres secs.
You can buy quality wines from the Yonne region for cheap. There are also antique stores and workshops both downtown and along the river.
Le Bistro du Palais,65 Rue Paris A former one screen cinema theatre, this is now a charming bar and restaurant with authentic Burgundy cuisine. They also have a wonderful local wine selection, and a piano.
If you want, to cook your own food or buy food for a picnic, Leclerc is the giant supermarket that has most of what you need, located on the Northeast side of the river (14 Avenue Jean Jaurès). As you are in France, avoid buying baguettes, wine or cheese in a large commercial store; try buying those kinds of products in a local boulangerie, cave à vin or fromagerie : the charm of these such stores is the reason that you came to France and something that you cannot get at a chain store.
Drink a beer or a café at the 'Annex' during (European) football matches. The regular crowd congregates to cheer on the local team, AJ Auxerre, whenever away matches are played, or a foreign team who plays a French player. An alternative to the 'Annex' is 'La Bodega', a pub that uses old wine barrels as tables and that has a huge projection screen.
There is a row of hotels, including some budget hotels, on a ring road on the outskirts of the city that is part of National Route 151. Part of the road is called Boulevard Vauban. The location is not bad as the city is small enough that a walk from that ring road to the old city and its sights is only a few minutes.