"We would like to do some shopping for souvenirs - not in expensive stores. Something reasonable and affordable. Could you advice us some good local place?"
If anyone wants to buy souvenirs - whether he is a local, a foreign tourist or a provincial Russian visitor - he has to go to specialized souvenir shops. Normal Russian shops which sell clothes, food or items for the house, do not sell souvenirs. I am serious. Inexpensive local places simply do not exist, I am sorry. If to go shopping there is no other sensible option but to go to a souvenir shop, which is in general oriented towards tourists but:
In case you think that there is some personal reason for me to offer this I am ready either to skip shopping completely, or to take you to any address you give me. But the reality is that I can take you to the least expensive of the tourist souvenir shops which has the largest choice of inexpensive items, but I'm afraid can not do better than that.