Please be aware that the cost of the Inter-Rail ticket does not include many high speed or overnight train supplements nor give easy accessibility to 'global fare' trains.
If you don't want to try and use the remaining overnight trains in Europe, don't forget that there is an option to use the 'rabbit hutch' type hotels pioneered by the Accor group (eg ETAP). Many of these are in industrial estates some way from railway stations, but there are some city centre ones - which you can identify with careful internet research.
For example, I have used the following 'budget' hotels near stations:
ETAP:
Switzerland - Basel Pratteln (short walk from Pratteln station)
France – Boulogne sur Mer, Tours, Toulouse, Strasbourg
The next level up is Ibis which is more expensive than ETAP but has many more hotels adjacent to stations:
France – St Etienne, Grenoble, Orléans, Marseille, Strasbourg
Switzerland – Chur, Basel SBB
In general, Inter Rail is much more difficult than it used to be when I was 19 (er in 1979...) and Inter Railed every chance I got. In those days nearly all trains were walk on and nearly all overnight trains had day coach seats for no extra fare. I learned that the key thing to do to get proper sleep was to have a good evening meal before travelling overnight.
