You can double the range of booming blade with Spell Sniper
The booming blade spell has a range of Self (5-foot radius), and I can see no reason why this can't be doubled to Self (10-foot radius) like any other spell.
However, even if we can double the range, the doubling is ultimately useless as the spell explicitly states:
[...] make a melee attack with it against one creature within 5 feet of you. [...]
Thus, increasing the range won't actually help us to target creatures that are farther away. This is similar to the case with the counterspell spell.
Booming Blade is intended to work with War Caster
A spell cast using War Caster must target only the provoking creature so if booming blade targets the caster, it can't be used with War Caster.
To borrow from an answer to a similar question and the intention for these sort of spells (a tweet from Lead Game Designer Jeremy Crawford):
- "Self": means that the spell targets the caster
- "Self (XYZ)": means that the spell is an area-of-effect spell, whose point of origin must be the caster
A note about D&D spells with a range of "Self (XYZ)": the parenthetical—which says "5-foot radius," "15-foot cone," or something else—means you are the spell's point of origin, but you aren't necessarily its target. You're creating an effect that originates in your space.
So such a spell, at least according to this answer and Crawford, does not target the caster and thus can be used with War Caster. Crawford has even explicitly explained the interactions between War Caster and booming blade:
Booming blade works with War Caster.
So the intent here is clear, and looking into the actual rules we do find the following:
Spells that create cones or lines of effect that originate from you also have a range of self, indicating that the origin point of the spell's effect must be you.
So Self (XYZ) indicates the point of origin and not the target of such spells and we're done, yay.
Unfortunately, this rule doesn't explicitly address spheres and a different rule states that "a sphere's point of origin is included in the sphere's area of effect". Because of this, it is unclear to me how this combination should work if we stick to reading the actual rules. There are countless questions about spell targets and AOEs across this site with people arguing every which way with plenty of upvotes held by everyone. This is an incredibly messy part of the rules.
At the end of the day, a GM is free to rule however they want. At my own tables, booming blade does not target the caster, its range can be extended by Spell Sniper, and it can be used with War Caster.