Where can you actually eat medieval food rather than a themed approximation of it?

The distinction you are drawing is exactly the right one, and it maps onto a real split in who cooks this food.

Themed restaurants sell an evening. The menu is modern food with old names, and the research budget went into the building. Fine as entertainment, useless for your purpose.

Historical reenactment groups are the opposite. Many of them take period cookery seriously, work from surviving manuscripts, and argue at length about ingredient substitutions. The food is the point rather than the backdrop, and it is usually far closer to the sources than anything commercial.

The practical consequence is that your best route is often not a restaurant at all. Look for reenactment societies, living history museums with working kitchens, and open days at castles and abbeys where the kitchen is part of the exhibit rather than the gift shop.

Germany and central Europe are the strongest region for the commercial version, because the medieval-tavern format there has been running long enough that some places genuinely researched it rather than costumed it.

The filter I use when reading a menu, which separates the two categories quickly:

• Does it name sources? Places doing real reconstruction tend to say which manuscript or period cookbook a dish comes from, because that is the interesting part to them.
• Are the spices right? Medieval European cooking of the wealthy used a lot of what we now think of as sweet spice on savoury food, plus verjuice or vinegar for sourness. A menu with tomatoes, potatoes, chillies or chocolate is not period, since all of those arrived from the Americas later.
• Is the sweetness in the wrong place? Sugar was a spice, not a dessert category. A meal that ends with a modern pudding has usually not thought about it.

That last one is the single fastest test.

One caution on authenticity as a goal: even careful reconstructions are working with modern ingredients.

The wheat, the meat, the fruit and especially the vegetables have all been bred substantially since then, and the fuel and the pots were different too. So the best available version is a well-informed approximation rather than the real thing, and the good practitioners say so.

That is not a reason not to seek it out. It is a reason to be sceptical of anyone claiming exactness.

Worth adding the option that is far easier than travelling for it: cook one.

Several medieval cookery collections have been published in translation with modern quantities worked out, and a surprising number of the dishes are simple — they were written for cooks who already knew what they were doing, so the instructions are short. A spiced almond-milk pottage or a period sauce takes an ordinary evening and no special equipment.

Doing that once also makes you a much better judge of restaurants, because you will recognise immediately whether what arrives at the table has anything to do with the period.