I'm starting a Strixhaven game and get to be a player for once, I've played around witha  few ideas but am very tempted to play a small (gnome) mindflayer character as a dhampir but couldn't deciede on a class/subclass to fit this whilst also babysitting three first level wizards... thought would be appreciated. I am happy with any class, but it does need to be pretty competent to protect the nerds (said playfully) - potentially could commit to full wizard party

Someone to help defend a bunch of squishy wizards? I think there's nothing better for this than a Paladin. Depending on how you want to play your Mindflayer, I think you could still stick to a lot of the "classic" Mindflayer traits by going for a Conquest Paladin, but there's also room for Vengeance, Oathbreaker, or even Glory.

Also, I like reflavored Dhampir as a Mindflayer analogue. I actually designed my own take on a playable Mindflayer homebrew some time ago, but it was before the Dhampir race came out.

Thanks TransmorpherDDS, I do quite enjoy Paladins so I'll have a look to see if anything is particularly synagistic there (Conquest seems the most flavourful). Also, just had a look at your Homebrew, and I think that was a nice stab at a rogue mindflayer, I like it!

Or possibly Psi Warrior

Cavalier fighters are good for protecting. They have one of the rare mechanics that makes enemies want to attack them. They can stop people getting past them. 
Pair it with PAM/sentinel and you can lock down a large area. 

Both Ancestral Guardian & Armourer Artificer would do a better job though if I want to be more than 5ft away… I could go for a tank build. Which I’m tempted by…

I’d like something synergistic though and sadly Monk won’t help much for protecting the Wizards. I love the idea of Dhampir so much, especially with a more Mindflayer vibe, but finding it difficult to make a build pop

Dhampir definitely feeds well into being a front-line fighter, since you have a unique self-heal Melee attack and Spider Climb for free to help you cover distance to reach targets that other melee fighters might not be able to reach.

One combo that comes to mind for me is going sword-and-board as a Paladin with the Shield Master feat. That way you can use the Vampiric Bite to give yourself a boost to your next ability check... such as a Shove with your shield to knock someone prone and then lay into them.

Although if we're talking about what class would actually feed most into the whole Mindflayer concept, I think the obvious choice is Aberrant Mind Sorcerer. Having an inert Mindflayer Tadpole in your system is outright listed as one of the premade origins for where the power comes from. However, it's not great for guarding a group of wizards.