Can you read a OS 1:25,000 map?
While GPS systems or mapping on phones makes life easier (including the OS app) there are a number of things that can go awry and leave you needing to read the map. Plus they're fascinating for reading and understanding the area.
I still like guidebooks for a starting point and context on finding routes if I don't know an area.
From Manchester I'd start with the Peak District as the majority is beginner friendly and tends to have clear routes. Mam Tor is very busy these days. Stannage Edge gives a nice feeling of height. Curbar and Froggat also have the millstone outcrops. I'd avoid the Kinder Scout area until being confident as navigating as the weather can do its own thing and you're potentially relying on subtle natural features and compass work over those moors.
For the Lake District, Catbells have a lovely mountain feel and beautiful views with less height and navigation skill required than most of the mountains. Most of the Lake District (and Snowdonia, also fairly accessible) are more technical.
Any upland area is likely to have more extreme weather than the valley, especially wind. Weather can change quickly so always be prepared for the unexpected. In addition to general weather forecasts, look up the mountain forecasts for more specific details.
What is your current fitness like? Are you used to walking up hills? Terrain, navigation and admiring views will slow walking pace down compared to urban walking.