My dad has just got a Kia Sportage – he's also just got a caravan so it's all bought to tow this mobile house around every couple of weeks/weekends – I'd be ranting at him if he had bought it without needing to pull the 1600Kg of caravan around.
4×4 in terms of Land Rover/Shogun/etc. isn't going to be economical unless you accept 28mpg is a good result. Saying that, the Astra VXR won't be far off that anyway so it might sound fine.
Unless you got for an older version, you will get hit for road tax for the 4×4 in that flavour, but something like the Skoda Octavia 4×4 isn't as bad – very practical as the carrying space is very good, has a bit of oomph about it but doesn't have the weight of the proper 4×4's so economy is better.
What do you need the car to do most? How do you want to carry your bike (on roof/boot/towball/inside)? How many people/bikes do you want to carry? Is the biking and dog duties your primary use of the car or are these infrequent? Are you look for performance as well as 'economy'?
4×4 is great fun but for most driving situations, it isn't needed – unless you are working on a farm or towing some real heavy stuff, it is unlikely to be a real benefit – the extra grip can be felt when you really do push it (but I've never found it to be much better than a 2wd car – apart from my VR4, but you had to do stupid things to make that go funny but the EVO Active Yaw Control stuff did seriously funny things so probably not the best thing to compare 'normal' 4×4's with)…
Just my thoughts, plenty of vehicles out there that will fit your requirements, just got to find them!