Apparently, this Brevet is passing my house at only 2kms. Never done it but the route itself will be completely flat, with most of it on bikepaths and smaller roads I assume. I think some nice roads and quite some variation.
If you will travel by train from airport to Eindhoven then Amsterdam will be easiest (trainstation is location underneath Schiphol airport and I think there is a direct connection to Eindhoven).
If renting a car, then Dusseldorf will be slightly closer (appr. 1 hr drive), followed by Brussels (1h15) and Amsterdam (1h30).
Hotel and restaurant will not be an issue, plenty of them in Eindhoven
Furthermore, I don't think you need full winter gear however I would use leg/arm warmers, light windvest and maybe a rainjacket, and definitely bring some light gloves and shoe covers (weather can be between 5C and rain and 20C and sunny, however mornings will def. be a bit cold without leg/arm warmers). Maybe a small mudguard as the concrete bikepaths will stay wet for quite long if there is some rain during the day.
Don't know how long you're staying; if you also want to have a swim, you can go to the Tongelreep (Pieter v/d Hoogenband swimstadium). see
https://eindhovensport.nl/tongelreep/zwembanen for lap-swim times.
Finally, if you intend some more riding, there's no reason to leave the Eindhoven area however you could go to Limburg( appr 50 min by car) or Ardennes (appr 1h15) if the weather is nice to ride part of Amstel Gold Race or Liege Bastonge Liege.