York is in the north of England, about half way between London and Edinburgh. It is well-served by trains, both from north (Glasgow, Edinburgh, Newcastle) and south (London, Kings Cross), and on the cross-country service from Manchester airport to Hull. There are also direct trains from major cities such as Bristol, Birmingham, Sheffield etc. All trains will carry bikes but check the conditions as different operators have different policies.
It is also easy to get to York by car, lying to the east of the M1 and A1 along the A64. The A19 from Middlesbrough to Doncaster passes through York
Of course you could get to the Solar System by bike! the model lies on the national cycle network route 65
There is an excellent cycle map of York available from the City of York council. The Solar system model is marked in top left-hand corner of square C9.
Find it on Google Maps here.