I am Squarer by the way - just on my way to bed and found this (I never usually get my name mentioned [filled with pride emoticon] Cheers Mandymac - large white wine next time is it?
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Head eastwards out of the city (bus numbers 25 or 27 if you are carfree. About a mile outside of the city on Carlton Road is a branch of the Co-op and if you walk down the road which runs parallel to Carlton Road directly behind the Co-op you will come across the Stonebridge City Farm (it's on Stonebridge Road). Its free to access, has a small outdoor play area, a cafe and sells suitable food for kiddies/parents to feed the animals (even their donkey is wonderfully gentle!)
A little bit further up Carlton Road (1/2 mile) is a further education college (on the opposite side of the road to the Co-op and that has a soft play area. I have never been to it, but a couple of friends of mine take their older kids to it. There is a babies/toddlers section by all accounts.
Wetherspoons on St James street (just off Market Square which is currently being refurbished) is good for taking young children to eat realtively cheaply. The majority of the pub is smoke free and there is so much room you don't have to worry about pushchairs etc getting in the way.
There is also Greens Mill in Sneinton which is a working windmill (if you do any baking at all I can recommend the flour they sell. Last lot I bought was some spelt flour and it is really nice). You can climb up the windmill whilst it is working (but the stairs are extrememly steep as you can probably imagine, look out the top etc, and there is a science museum which is great fun for kiddies to explore/whack at.
I just had a look for a site I had saved in favourites, but it has just changed format - it used to be better days out in Nottingham and has expanded to the East Midlands. Still got the same \link{http://www.betterdaysout.co.uk\useful stuff} on there though.
Where does your SIL live? If you have a look at the link I have given you, I will give my opinion on anything you are interested in if you like 