West towards Paris
From Place de la République take a bus number 29 to Buchoz and from there a bus number 106 to Champ Banal (ask the driver to announce the stop for you). Once off the bus, start walking along N43 (Rue de Metz) in the direction or A4 (you will already be able to see it). Keep walking almost up to the very intersection and right before it take to the right onto a dirt road on the side of a field. Walk this dirt road alongside A4 and you'll see a service station around 500 meters ahead. Cagatay went there all the way by walking and it took 3 hours.
North towards Luxembourg, Brussels, Trier
Take bus number 6 that goes from Place de la République (bus stop next to Galleries Lafayette in the city centre) to La Maxe. The ticket costs 1.20 EUR. Doesn't operate on Sundays, here's the schedule. Get off at the stop Goujenotte beside the massive IKEA shopping centre and walk down the road until you see a roundabout and an ESSO service station nearby. Walk down the ramp until you reach both of the exits. One hitchhiker got a lift within 10 minutes while standing between the ESSO petrol station exit and a motorway exit. There is a lot of international traffic in this region.
Take a bus number 6 from Place de la République direction La Maxe and go to the last stop (1,20 EUR). From there walk west, walk over the motorway and walk further on the same street around 2 km until you see the petrol station. When you see the petrol station, it is better to walk about 500 metres further and walk into the station along the motorway (there's a little path that will bring you on the motorway. From the petrol station, it is easy to get rides directly to Lyon or even further.
East towards Saarbrücken, Frankfurt or Strasbourg
From Gare SNCF (the main train station) or Place de la République take the bus number 8 or U to Technopole (both stop next to lake Symphonie - ask the driver). From there walk to Grigy (part of Metz). Once in Grigy, keep on walking along D955 outwards the city center (follow the signs to Strasbourg). The road goes slightly uphill on top of which there's a roundabout right before the short bridge over the motorway to Nancy, then another roundabout. Stand just right after the second roundabout (one hitchhiker tried three times there and never had to wait for more than 20 mins). If you go to Germany make a sign for Strassbourg and then get off at the peage which is about 30 km away. You can also make a sign saying A4 Est - Peage
North, West or South (Luxembourg, Paris or Nancy)
It is possible to get a ride towards these three different directions by standing on the Avenue Joffre, under the bridge, in the western part of town, very close to the city centre. It merges with the A31 300m further. Always use a sign here.