This may be of help to anyone visiting Uppsala, including those with children. We've been to Uppsala twice and found out about it only on the last day of our second visit - neither the tourist information at Arlanda nor at Uppsala told us about it.
It gives you
• free admission to most if not all the main museums in Uppsala;
• free transport on the green city buses, yellow regional buses, and the Uppstaget train within Uppsala, and on the 801 bus and the Upptaget train to and from the airport (the additional airport charge of SEK 75 still has to be paid when travelling to and from Arlanda Sky City by train); and
• free parking in designated municipal parking spaces.
It costs SEK 195 for a day (I don't know whether that means it runs from midnight to midnight or for 24 hours from when you activate it, as the travel pass in Stockholm does), and is valid for one adult and two children up to 15. Best of all, there is an autumn offer - and a summer one I think - whereby if you buy one card you get another one free! Given that it costs SEK 180 for two on the bus from the airport, it's a pretty good deal.