This is arguably the least attractive part of Fife, and only the most detailed explorer, or one with special interest in specifics of the area, would devote much time to it. Apart from the Deepsea World aquarium in South Queensferry (just by the bridge from Edinburgh), the nearby Culross and Dunfermline are the only places really worth a decent look.
The former is a picturesque burgh with an attractive Palace (a house, really) and another of those atmospheric, ruined Scottish abbeys. The latter was a capital of Scotland for a substantial part of its history and although it very much went down in the world since, it holds several significant historical monuments.
A centre for the Culdee faith in the 6th century, Dunfermline was for a time a capital of Scotland, a seat of its Royal Court and an important centre of Christianity. Notable sights include a ruin of the Royal palace, a a favourite residence of many Scottish kings, and a nearby Dunfermline Abbey, partially ruined church and priory dating back to 11th century. The abbey church is pretty impressive and the ruins, as often is the case with Scottish ruins, give a good impression of the building's former glory. The undecrofts of the Palace are the most unusual and well worth exploring.
Dunfermline also advertises itself as a place of birth of Andrew Carnegie and there is a rather embarrassing monument to the man, consisting of the cottage named, yes, correct, the Birthplace Cottage and a large Memorial Hall, all devoted to celebrating Carnegie's life. The museum has been modernised and relaunched recently and anybody interested in industrial tycoons turned philanthropists can explore the life and times of Carnegie, saving-gracely, free of charge.
This area of Fife was important part of the Fife coalfield and 53 pits were open at some time. The last one closed in 1988, and the feeling of post-industrial gloom still blights the area. There is a string of industrial - or rather post industrial - villages that are scattered in the countryside in this area and which also line the coast of the Firth of Forth from Rosyth to Leven, some of them with a bit of a sea-side resort reputation, but in all honestly, they have little of interest to a typical visitor and possibly even less as places to live in, as large swathes of council estates and some of the lowest property prices in Fife testify.
Aberdour castle, in the eponymous village located between Dalgety Bay and Burntisland, is also worth visiting if you have time and are in the area, as it's an extensive site with a very good educational program for children (though it's possible you need to be a part of a group to take a full advantage of this).