"I can't imagine there is anything like Radio 4 in the commercial world."
Some time ago, on a Sunday morning "Broadcasting House", some (American working in Britain) compared the BBC with the funding mechanisms for 'public radio' in the USA.
Over there, many talk or music stations are affiliated with NPR.org and/or PRI.org and have quarterly "membership drives" with various levels of subscription for individuals (and in tandem with supporting your local station, you could promote them too, with the 'free gifts' of coffee mugs, T-shirts, thermos flasks and so on, or just getting a 'free' subscription to NewsWeek. Some provide membership cards which can get discounts at shops or events.
NPR and PRI put out a whole range of great programmes, from comedy and specialist interests like gardening or cooking to variety programmes now missing from the BBC. Take a look at a few of the 'talk' station schedules and while it won't have the massive number of programmes (or lots of 15 minute shows) the way Radio 4 does, you will see lots of variety in content.
There are 'sponsor' messages, simply naming various large corporations, but the short slots in some shows include news headlines, weather and similar, rather than the sort of 'commercial' adverts one might hear on a commercial station (and in fact those are fewer and further between - lots of messages are from government and advice services now, from what I heard recently).
Of course there are hundreds of stations across the USA, and some of the "public radio" stations are run at universities, playing music (classical or jazz, most likely, though some may have regional groups as a major part of their playlist - WTMD.org used to play smooth jazz [I have 2 CDs as gifts, for being one of their few overseas listeners], but changed to have more popular music). Lots are news/talk (but not of the old LBC style). While the content is very much tied to the continent of America (so the news show is something of a loop for 4 hours to cover all time zones) and wouldn't directly fit a UK situation, the overall funding and networking of should could be done here very easily (many of the commercial pop stations network their shows for large portions of the day, so the BBC doing something similar would be no problem - they already have the infrastructure built for it).
Take a listen to some of the US stations:
www.wypr.org Maryland
www.kcur.org and www.kunc.org - mostly music in the week, but have a lot of variety of content at weekends, well worth a look.
www.wbur.org Boston
www.vpr.net Vermont Public Radio (New England)
www.kalw.org San Francisco - carries West Coast Live on Saturdays
Prairie Home Companion, Whad'Ya Know and West Coast Live cover music, literature, comedy - true variety shows.
Look out for some of the stations having a "Pledge" button - they're currently asking for funding and show a genuine enthusiasm for working for their community rather than for a fat pay cheque. Wish more 'talent' on the BBC did that !
Also for any night birds who want to listen to something other than Five Live or World Service - try one of the above, or the American service of www.wrn.org (World Radio Network) - they have 30 and 60 minute slots and fill day and night with English programmes from stations worldwide, so you will hear European and other material... Some will be slightly touristy, but much will explain local traditions.
Sorry - long and rambling - but there are too many stations and shows to mention.