Somerset House is often missed by many people visiting central London. It's a beautiful building, with a variety of galleries plus a nice terrace for enjoying a drink! It's only a 5 minute walk from Covent Garden
http://www.somersethouse.org.uk/
Just across Waterloo Bridge from there is the Southbank Centre. There's often free music going on (either outside or within the Queen Elizabeth Hall or the Royal Festival Hall) and, again, it's a great place for eating and drinking on the terrace.
http://www.southbankcentre.co.uk/
£13.90 might seem a lot to visit a garden but I can assure you that you'll find the entrance fee to Kew Gardens is actually a bargain. It's easy to spend all day there!
http://www.kew.org/vi...ld-with-kew/index.htm
Greenwich is great (especially if you travel there by boat):
http://www.visitgreenwich.org.uk/
North London? Well perhaps hubby might be able to overcome his distaste for museums in Hendon?
http://www.rafmuseum.org.uk/
or you could simply go shopping in Camden Lock market:
http://www.camdenlockmarket.com/
Chris