I have bought some baby shoes at NuggiHuus (next to Aeschenplatz), but they don't have a big selection and it's only for children up to 2 years old. I would go to Manor or to "Du pareill au meme" (Falknerstrasse). There is a shop where they only sell children's shoes in Munsterberg (but I don't know the prices in this one).
Schuhhaus Klybeck on Klybeckstrasse 11. Have good brands at almost 1/2 price. Last year's colours and models - if you're not worried about that and a rather small choice, then you'll get bargains there. Oh, more girls shoes than boys shoes. Shoes for adults, too.
The one on Munsterberg is quite good - but expensive; at least for us as our 2 y.o. has particularly wide feet. In the end there were only 2 pairs of shoes in the whole shop that fitted.
if it's not too far from you, you could try in Lorrach. There's a nice, big shop, I have to check the name, but it's in the center of the town, easy to find. And then you have some money back (VAT).
I bought a pair of Nike for my son from Vogeles, for 50chf and it was so good. Worked well for 2 years and now turned small. But still looks good and new.
I have to say that maybe the only thing that is not too expensive here is shoes and they do have a good selection. at least compared to NL...Vogele is OK and they carry some good brands as nike or sketchers...
Drochenbach (sp?) In SBB has nice shoes. They have the same shop in Marketkauf (Weil am Rhine). As well, if you're looking for Nike, Puma and others you can try the sport shop under FLY (Leimgrubenweg 27) they're having a sale right now and can be picked up for 25chf - 50chf.
Another I thought of as well, if you go to Weil am Rhine, Hauptstraße, their is a medium shopping center (has Muller and Aldi...ect). There is a Baby Waltz there and they have a small, but nice collection of children's shoes.
Look out for a shop that sells "Elefanten" shoes, that's THE German child shoe brand, prices are reasonable. These shops also have a foot measurement system for children's feet.
For kids shoes Reno is definitely the place to go.
They measure the inside of every kids shoe they put on the shelf and give it a standardised "Reno size" so that you know that if your child is measured as a 25 then the shoes they are trying on are actually a real size 25. Amazingly there can be up to two sizes difference between the reno size and the makers size marked on the shoe.
They also have some really fancy machines with imaging to measure little feet. And staff are very into measuring kids feet and checking shoes fit.
There are a few in and around Basel - there's one just up from Claraplatz (towards the Messe) and there used to be one in the same building as Thalia in the middle of town - not sure if it's still there though (I don't tend to shop in town these days).
There is a list of Children's Flea Markets happening around Basel, where parents sell (often hardly) used stuff. You can also sell your old stuff, or exchange it. Here is a list.