Good Footwear
I'd need to find the article, but there's an observation that humans are continually breaking world records for speed and endurance.
The hypothesis is that we are not evolving, but that our equipment (shoe padding, soles) is getting better. It requires less energy for us to run, so we can run faster, further, and longer.
Looking at this chart alone, and taking the hypothesis for granted, your traveller would get a +25% boost to his/her single mile running time.

A Good Running Suit
There was a huge change between the wool heavy-weather gear of the early 1900s, which had been the standard for a long time, and what is modern.
Modern clothes resist getting wet (avoiding foot rot or freezing), they dry quickly, and they retain more heat. Modern clothes are made of synthetics that don't rot, or allow mold to grow on them.
They are lighter weight, more flexible, and take up less space.

A Modern Sack
Nylon has five times (5x) the strength of cotton, per unit of weight. It's also significantly less bulky.
A sack made of modern materials will better protect the things inside it from the elements. It will be able to hold more things. And it will have modern ergonomic thought put into it's design so that the load is balanced, making it feel easier to carry your equipment.

Knife Resistant Shirt, Gloves, Hat, Hoodies
We have technology that pretty well foils your typical medieval small arms without sacrificing any flexibility or looks.
Easily worn over your running suit and under your chain or plate mail.

Polarized Eyeglasses
Medieval types wore eyewear. They even sometime wore tinted eyewear (Nero, Seneca - per here) to help with the brightness of the sun.
With polarized sunglasses not only can you cut down on glare.
You can see clearly through the reflection on water.
You can also see clearly through haze, in certain conditions.

Hearing Aids
Hearing aids can be extremely discreet, and increase the volume of distant conversations by 500 fold (+15 dB)

Tankless Breathing Apparatuses
Small enough to fit in your pocket. Current technology allows only to store an extra breath (maybe 2), which still extends your time underwater from human to 2x or 3x human.
Technology is under development to extract oxygen from water like gills, extending indefinitely the amount of time you can stay searching underwater for wrecks, artifacts, or just hiding from people on the surface.
Also conveniently looks like a stick.

A Good Ghillie Suit
For disappearing or getting close to something you're not supposed to, there still is really no substitute on the original.
Made out of modern materials, however, you could fit it into more discrete storage spaces; not need to worry about mold or rot; and it probably is lighter and breathes better.

An Invisibility Cloak
Ok. Maybe this one is a bit too far, but it's just too cool to pass up.
Sheets of lenticular material that can be curved into free-standing shields, shelters, or walls.
If you need to disappear. Really disappear. This works.
Does not work well in brightly-lit settings.
(not me. pay no attention to the caption)

A Lexan Shield
Lexan has half the strength of steel at ${1 \over 8}^{th}$ the weight. It doesn't need to be stronger (although Kevlar is available) because Lexan can handle the full range of melee combat arms.
Unlike steel bucklers, Lexan bends. Your fellow knights might laugh, but a "special wooden" shield that bends like this hurts a lot less receiving blows. The energy of the hit is mostly absorbed by the material, not translated to your arm. As a result, you can endure hours of punishment without being particularly winded.

A Good Stick
It's a surprising outcome of the United Weapon Masters tournament -- a modern tech gladitorial games using modern equipment -- that the most effective weapon is... a good stick.
A long, flexible stick reaches around swords and bends around shields to fatally strike the top of the head : a vulnerable spot, even when protected with a helmet.
With this bit of modern insight, you can defy traditional medieval "brilliance".

A Boron Nitride Sword
Near future tech. Boron nitride blades are used to cut diamonds, but I don't believe they are yet used in sword making.
Image below is what a sword of double the hardness can do to a lesser sword.
Boron nitride is 10x (60 GPa) as strong as mid-grade steels (4 to 8 GPa). Using the image as a guide, a boron nitride blade with a good edge will slice through lesser weapons and armor with frightening effect.
It might be a blade you wouldn't want to use often, because it would draw attention.
