panning across lyon from west to east, or chronologically from roman to modern times (which is the same thing)...
the amphitheatre on
fourvière, and other roman stuff strewn around the top of the 5th arrondissement is worth looking at. depending on how much roman stuff you've seen or will see elsewhere, and how much your interested in antiquities, the aqueduct out at chaponost, even a run down to vienne (20km) may be in order. even if that's not really your cup of tea, the view from the basilica is not to be missed.
you get up there on an old cable tram, but it's a very pleasant walk back down to
vieux lyon. the place got so decrepit that no one touched it for the longest time, in fact it almost got knocked down in the early 60's to make way for a freeway. all's well that ends well, and now it's one of the purest medieval
cum renaissance quarters in europe. things to see there are st. jean cathedral and the twisting semisecret passageways called
traboules... get a guide to them at the tourist office (or on internet). vieux lyon is a good place to stop for lunch, there are lots of places for all tastes and budgets. avoid
le sol, since tapas are done much better where you're headed. if you are used to eating tripe and such, traditional lyonnais cuisine is done very well at
la machonnerie. vieux lyon also has our best british style pub, the
saint james.
any bridge over the saône gets you to the
presqu'île, which is the center of town. lots of nice 19th century buildings, two big plazas: the
place bellecour which is mainly just huge, and the
place des terreaux, which has lots of cafés and a fountain by bartholdi, of statue of liberty fame. up the hill from there you get to the
croix-rousse, a town within a town, which i know nothing about, but gnafron lives up there so it can't be too bad. note that in the presqu'île it's nice to have dinner in the
rue mercière, which is almost one continuous sidewalk café. a lot of lyonnais look down their nose at it, which is their loss as far as i'm concerned.
if you keep heading west you cross the
rhône, second of lyon's three rivers (the third is the beaujolais

), which has very nice views, especially when everything's lit up at night. and you can rent a velo'v for a very nice ride on the banks from
the parc de la tête d'or (a mini central park) and the
parc de gerland. beyond that... well, even though i've always lived
rive gauche, there's not much there for tourists, except the part-dieu and the train out of town.
bon voyage!