Some of the ridges around Winnat's Pass would be a reasonable shout along with some of the cloughs on Bleaklow etc (particularly thinking of Wildboar Clough). Otherwise head to North Wales or the Lakes and you have acres of good crags for this purpose.
I started climbing on Dovestones Edge in big boots. There are plenty of routes enjoyable in that type of footwear. As to polish, if it attracted Stanage type numbers it would be a problem but an islolated visit from someone isn't going to damage much of anything. And absolutely no-one will complain if you wear your boots in the quarry, Waterfall and Black and White Traverse being perfect big boot routes.
many of us started climbing in 'big boots' - my first climbs were at Frogatt in a pair of Hawkins walking boots and it was a while before I saved enough to buy a pair of EBs
For near Manchester, I'd say Alderman Rocks would suit your purpose well. Quite a lot of easy routes and scrambles, with a vaguely alpine feel (the style of the climbing).
PS. You could combine with Dovestones; e.g. Dovestones in morning/early afternoon, Alderman in evening.
Cheers need to get the confidence for climbing alpine routes with big boots will give it a bash in this glorious Manchester weather we got at the moment ☀️☀️
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