Nenn es nicht 'mappen', sondern 'spazierengehen' oder 'radfahren'/ 'eine Radtour machen'. ;)

I can recommend the iBlue747. I bought it from a Ebay-seller in Hongkong for EUR 60 (incl shipment).
* It uses Nokia-rechargables. Battery lifetime is longer than a day (24h).
* Storage is 4MB internal memory (commonly advertised as 32 MBit - so don't be disappointed! ;) )
* Size is about same as a matchbox and weighth due to the battery about mobile phone
* There are GPL-licensed communication softwares for the device as well as some proprietary Windows-stuff from the manufacturer.