Honestly, I can't get my head around Bladesinger.
They're certainly not the worst Wizard subclass, because they're not Enchanter, Conjurer or Transmuter - the Bladesinger L3 feature alone is better than all of their features except the Conjurer's damage free concentration (MAYBE).
But how are you actually supposed to stat them? Some of the backgrounds for it mention using a Longsword or a Warhammer, but holy fucking shit, how the fuck are you supposed to use that kind of weapon with Light Armor only to be in melee? You basically NEED that fucking Finesse melee weapon, so you're stuck with 3 realistic choices:>Shortsword = Scimitar
Can be dual wielded without a feat.>Rapier
The most natural choice, but Jesus Fucking Christ, 5e is so fucking biased in favor of Rapiers. Rapier this, rapier that, every fucking Dex faggot uses a Rapier if they don't dual wield.>Whip
The most interesting and legit looking choice. Rogues do not actually get proficiency with Whips, so they can never use them without multiclassing or sucking the DM's dick. As a full caster, you can also benefit MUCH MUCH more from Spell Sniper, which is necessary for Reach booming blade.
So, is that basically it? A Bladesinger is just a normal Wizard, except he maxes Dex along with Int, instead of maxing Con along with Int? So that he can sometimes use his Whip Booming Blade instead of casting a Spell? The Extra Attack option is mostly wasted, because it's rarely more beneficial than Booming Blade.
In a way, it looks like as a Bladesinger, you should just get 5 levels and (for early level 3 spells/haste) and then move on to Rogue->Arcane Trickster.