Not sure exactly where you are located Tom, but I live in Rednal, and here's my tuppence worth.
I use the route into town a lot via Longbridge, Northfield, Kings Norton and onto the canal through Selly Oak and into town. Where as you know there's lots of caffs, and access to the canal network out to Wolverhampton or across to Small Heath and beyond. The reverse direction of course takes you out to the Lickeys. For a short trip while you get used to cycling, you could do worse than take the canal out to Bournville Station, divert off it to one of the caffs on the Pershore Road and then return the way you came. Big plus is if you are tired there are frequent trains and you can just pop the bike on to go back. Even better if you are an old fogey like me, and have the free bus pass!
I also divert off the route sometimes along the Rea Valley route through the back of Selly Park (parallel to the Pershore Road), and through Cannon Hill park where there are 2 places for a cuppa, one of which is the Mac. Don't like the road route much though around the back of the cricket ground and through the red light district, and especially not the contraflow cycle lane back down Hurst Street.
If you have a car then a trip out to Earlswood will reveal some pleasant cycling, and also lots of cyclists! Mainly 'cos its nice and flat out there. A trin will get you there as well. And there's plenty of refreshment stops - Manor Farm do a cyclists breakfast!
Another option is the train to Sutton, the station there is close to Sutton Park, a great place to find you feet on a bike (or find your pedals for that matter!)
I've even taken the train out to Hednesford, then cycled over to the heritage trail on Cannock Chase. Or again, if you have a car park at one of the visitor centres - Birches Valley (Near Slitting Mill) is one of my favourites, you get access there to trails that are as easy or as challenging as you like.
There's a leaflet you can get - try this link - I haven't got a copy but I'm sure it has loads of ideas.
http://www.birminghamcyclinggreenways.co.uk/
If you do fancy a group ride it may be worth looking at what PushBikes or other groups have to offer
http://www.pushbikes.org.uk/ - assuming Pushbikes still do family rides. Or a local CTC group maybe.
I could go on, but I won't!
Have fun - Richard