As has been said, there is a new reserve at the old RAF Woodhall site, but this is only accessible from Woodhall Spa itself. It is run by Lincolnshire Wildlife Trust and you can get information from here:
http://www.lincstrust.org.uk/woodhall-airfield
Have not been there yet as the walk entailed is, for personal reasons, not possible at the moment.
Dependent on what transport your have there are plenty of sites not too far away. The River Witham is a good place for a walk, though there haven't been that many birds along there recently. You can get good access at Stixwould and Southrey, and the path is very good for walking, and there are plenty of seats. The path is actually the old railway track and is now a cycle and walking path known as the "Water Railway". You can get all the way from Bardney to Kirkstead Bridge on it, and also from Bardney to Lincoln in the other direction.
Away from Woodhall, but not too far, there is a hide at Fiskerton Fen, see:
http://www.lincstrust.org.uk/reserves/fiskerton-fen
Slightly further afield there is Frampton Marsh RSPB Nature Reserve:
https://www.rspb.org.uk/reserves-an...eserves-a-z/reserves-by-name/f/framptonmarsh/
This has many hides and a very decent visitor centre where you can get a good hot drink when needed.
Even further afield, on the coast, is Gibraltar Point, see:
http://www.lincstrust.org.uk/gibraltar-point
It has a great cafe, but this is some way from the main hides for seeing birds. A trip back to the first car park and some walking will give you access to some good hides and a good selection of birds.
If you are interested in butterflies and dragonflies then a trip to Snakeholme Pit might be worthwhile, see:
http://butterfly-conservation.org/2401-1896/snakeholme-pit-lincolnshire.html
or not far from that is Chambers Farm Wood, which has a butterfly garden and there are excellent walks through the woods where you can see different birds, see:
http://butterfly-conservation.org/5369/chambers-farm-wood-butterfly-garden.html
Hope this helps a bit, even though its a bit late, others may find it useful.