There are options available to you as a Wizard (BladeSinger/Eldritch Knight) that will allow you to throw your weapon and 'teleport' to it's location.
There are also several pieces of information that will be useful to you with regard to how to do this that I will outline below.
- Throwing your weapon - Under Improvised Weapons (PHB 148), there is direction for providing ranged attacks/throwing melee weapons that don't have the ranged property. These rules can be used for attempting to hit a specific space.
If a character uses a ranged weapon to make a melee attack, or throws a melee weapon that does not have the thrown property, it also deals 1d4 damage. An improvised thrown weapon has a normal range of 20 feet and a long range of 60 feet.
Note: Your DM may run it differently for how to throw your weapon (action cost, range, etc), but this gives some potential guidance to that conversation.
- "Teleporting" - Here's where it gets more interesting. The options aren't immense, but there are some available to you that allow to "move" from your current position to the position you've thrown your weapon. They include:
- Misty Step - 2nd level spell, 30' range you can see, bonus action to cast. This may be your best option - especially if your DM requires an action to accurately throw your weapon.
- Dimension Door - 4th level spell, 500', Action to cast. This spell gives you significantly more range and capability, but it takes an action and a higher level spell slot.
- Teleport - 7th level spell, anywhere, action to cast. There are some other requirements as well, but given the high cost of this, I don't think it's what you're looking for.
- Helm of Teleportation - Rare magic item. This helm gives you up to 3 Teleport castings/day.
- Cape of the Mountebank - Rare magic item. This cape allows for one cast of Dimension Door/day.
- Ring of Spell Storing - Rare magic item. If you can cast Misty Step, you could have two safely stored in the ring for use without expending any spell slots.
- 6 class level dip into Monk - Way of the Shadow Given that you're already multiclassing into Fighter, such a deep dip into another class likely isn't reasonable. If you do it, then you would be able to use Shadow Step (PHB 80) to 'teleport' from shadow to shadow (dim light/darkness) up to 60' a bonus action AND get advantage on your first melee attack you make before the end of the turn.
Once you are in the space that contains your weapon, you have a couple of ways to pick it up: Either through a Free Action (PHB 190.) Please note that if you have misty-stepped to the location, you no longer have a bonus action available to summon the weapon to you.
When figuring out how to do this, please also think about the why. Roleplay is an excellent reason, but many of the ways to do this are an expenditure of limited resources to do something you can generally do by moving. That decision to do so is absolutely fine, but consider why you're trying to do something as well as how to do it.