Hi. Namechanged regular (to reply to you).
Echo others: I wouldn't live in Boston. It's miles from anywhere else and not very desirable in itself. Grantham and Sleaford are mixed places but are much better connected to get out to Nottingham or to the A1 north or south.
We've lived in and around Lincoln for years and now live right in the centre; we love it. Obviously it's not some great metropolis but there's heaps going on culturally compared to anywhere else in the county. Lovely shops, lovely views all around, loads of sports, music, theatre. I wouldn't live anywhere else in the county either. (Having said that, Horncastle and the Wolds are gorgeous but you are miles from anything else or getting to anywhere else in the country).
With that in mind, I'd recommend Lincoln itself if you can afford a nice property uphill OR the following clusters of villages: North East such as Nettleham, Welton, Dunholme looking to use either William Farr (outstanding comp) at Welton or QEGS at Horncastle for secondary. Or Branston, Heighington, potterhanworth looking to use Branston Academy (outstanding comp).
OR, if you're not worried about single sex grammars and dc are likely to pass the test, you could look at the Grantham or Sleaford grammars, but I'd still live halfway to Lincoln for the better facilities.
LSST is a great and highly sought after school but is very difficult to get a place at and has a complicated admissions system of feeder primaries. Can be easier to get into in later year groups than year 7.
If you live in Lincoln itself, though, your secondary options are more tricky than living in catchment of the best village comps: there's' LSST if you can get in, Lincoln Minster if you can afford independent or bussing out to Branston, Wm Farr or one of the grammars at say Horncastle or train to Sleaford (I know there have been low birth rates and therefore spaces in some of these schools in current yr 7/8 ish).