Perusing the website of the Roscoe Head, the only Merseyside pub to appear in every Good Beer Guide, I came across this Georgian Quarter Pub Crawl, helpfully provided by the pub for your entertainment. It features nine pubs (including the excellent Roscoe Head itself); I've tried them all at some point and each serves real ale. The various pubs have very different characters, from the gin house splendour of the Philharmonic (with one room called Brahms and another Liszt ~ devilishly subtle Scouse humour) to the bohemian ambience of Ye Cracke, where we used to go for a drink after union branch committee meetings years ago. If you get peckish part way round, the food in the Everyman Bistro is particularly good. The Everyman also has a folk club which meets every Tuesday evening at 8.30 pm in the third room.
Rather than reinvent the wheel and compile a similar crawl myself, I thought I'd just put a link to it. If you try it, have fun!
The Rocoe Head is about 10 minutes walk from Central Station ~ slightly more from Lime Street.