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Just knocking about ideas for the weekend, family member is taking part in the rally at New Brighton, wondering about parking up some distance away then riding with the kids see a bit of the rally then ride back. Maybe park near Meols or leasowe lighthouse and take the prom all the way there? Or any better ideas? kids 7 and 8 so a flat 10 or 12miles is probably their limit. I don't know the area at all, just had a quick look on google.
Park in Liverpool, near the Albert Dock, and take the ferry over to Seacombe. Then it's a couple of miles along a traffic-free route to New Brighton. Quite an adventure for little kids (of all ages)!
The wirral way is fantastic if its dry . Pick it up around West Kirby and ride as far as you want along the coast towards Parkgate.
http://www.visitparkgate.co.uk/wirral-way-country-park/4564767899
Leasowe lighthouse to where the rally is is about 3.5 to 4 miles, so you could carry on to Seacombe Ferry which is another 2.5 miles. Giving you an out and back trip of 12 miles or so. The prom is almost totally flat apart from one small gravelly/sandy hill when you get to Leasowe foreshore. It wouldn't be much fun on a road bike, but it's still doable.
Or as the previous poster said, if you're staying in Liverpool come over on the ferry, ride to New Brighton and watch the rally for a bit and carry on to Leasowe or Meols. There's a pirate ship built from driftwood at Egremont and you can get ice creams and a meal in New Brighton.
Prom is great for cycling, my kidslove the pirateship, bit younger at 6 & 8 tho
With ferry ticket you can get a discount on Spaceport
which was good fun, look out for discount deals
A lap of Thurstaston then ride via West Kirby, Hoylake etc. Not sure if that’s too far but lovely views from up on the rocks.
Park at Seacombe ferry for free, then ferry across to liverpool andalong prom to Otterspool and return, then onwards to new brighton. or park at Seacombe ferry and turn right down promenade to new brighton and return, then ferry over to liverpool and return, bikes go free on ferry , blunt end of boat has plenty of space.
https://www.merseyferries.co.uk/cruises/river-explorer-cruise/Pages/Ticket-Prices.aspx
or to save a bit of cash get a savaway ticket from any railway station or pay point, shop, allows a free journey on the ferry, ask for a boarding pass at ferry terminal.
https://www.merseytravel.gov.uk/tickets/compare-tickets/pages/saveaway.aspx
Wirral Way or an adventure to Hilbre Island and back to West Kirby would get my vote with kids.
Little did I know when living up there as a teen in the mid to late 80s, but there are a handful of cat4 hill climb routes from Lower Heswall to Heswall, think my "cycling life" would have been so different if Strava existed back then!
View from up on the rocks at Thurstaston

cheers for the ideas everyone, we'll see what happens.....
cycled up there today rain and wet, quite a few odd bods watching cars drive fast along a road and turn round and come back again.