I personally dont like going on walks, but maybe thats cuz im a teen. Anyway, different people, different opinions.

 

You can just go for a walk through the parks I've advised you to visit, a lot of them are big enough and interesting enough (of course they're all interesting but its not always a big enough park to go for a walk). The Jardin Botanique I think is the best for that sort of thing.

 

But there is the lake. I really like to take a walk around (at least part ;)) the lake, its calming (romantic :3) and very pretty. It has the mouettes zig-zagging along it so you can take a yellow boat back to where you came from easily.  It also gives you an insight of the beaches and the sorts of things you can do, like windsufing and sailing, because you will/or are bound to walk past them.  In the summer you can also make loads of stops at the limitless eating and drinking places lakeside ... 

 

Carouge is an interesting suburb of Geneva to walk around.  This area used to belong to the Sardinian royal family and so has an italianate flavour in terms of architecture.  Lots of little secret courtyards, lots of artisan workshops - definitely worth a wander.

 

And lastly of course the Old Town is full of interesting sights and squares and mustn't be missed.