My sci-fi civilisation has discovered how to make things out of unobtainium. Because of Quantum Space Magic, it is (for this purpose) unbreakable, perfectly reflective, and completely inflexible. The obvious difficulty of making "invincible" armour from this is the vulnerability of the joints, as they clearly can't be made of unobtainium - how could I design a suit of armour that could mitigate this problem as much as possible?
Design your armor like a hard suit. It won't be perfect, but anything trying to get it will have to get through some tight corners and tiny crevasses. It will be invincible to almost any practical projectile, though I'm not sure how it would hold up against really intense radiation (think ship-killer lasers; anti-personnel weapons should be no issue).
Like the sun crusher, your (second) biggest weak points are going to be the sensors. (Or the visor, if for some reason you want everything but the user's face to be invincible.)
You biggest problem (thank you Starfish Prime for pointing out that I'd overlooked the obvious!) may be cooling. As was discussed in another question, a heat-proof, radiation-proof material is bad news for anything inside it. Thermodynamics is a harsh mistress and dictates that if you're using energy at all, you're generating heat. If that heat can't escape, it's eventually going to have deleterious effects on whatever is inside the armor.
Now, you could work around this by giving your unobtanium reasonably good conductive heat transfer, but if you do that, you've also opened up a potentially significant vulnerability. If you don't, however, you're going to have to "soak up" waste heat somehow, which means eventually you have to exchange it, putting a time limit on how long the armor can be used. (Or, alternatively, you could have very vulnerable heat sinks on the outside...)
Your bigger problem is hammers.
Contrary to RPG lore, ancient armor was not usually addressed by ye olde canne opener, but by the war hammer, in whose steely light every unobtainium-armored warrior is going to look like a nail. Unless your quantum space magic has allowed you to make armor pieces with inertial dampeners, the joints are just going to be places where your body starts moving quite abruptly.
A solution to this, which also "covers" your joint problem, might be to be able to lock down the armor in response to attack with sliding rods that root the user to the ground. Still, there's an obvious response to that: turn a fire hose or a brigade of boys with slingshots on the armored miscreant and see how long the armor stays locked down. If it's much time at all, just have someone walk up and chain the invader securely to an unobtainium peg in the ground, to be left as an exhibit to the glory of your empire through the coming generations.
You wear an Unobtanium chainmail below the plate Armour
You know, one thing that can be obvious when you look at plate Armour, even at the late medieval period, is that there are places it doesn't cover all the time, which at first sounds like a problem in design. Something that might not be immediately apparent though is that said armors were developed for a reason: protect the wearer as much as possible without turning them into a clunky humanoid thing that can barely move and that wouldn't be able to get up if you pushed them down, which some people still believe was the case. However, plate armor still allowed you to move in it, as one can clearly see in videos such as this one. This was so that they could be well protected all while still being able to move around nimbly, which is absolutely critical for ANYONE wearing any kind of armor, because every armor will inevitably have gaps, from the gaps in the joints meant to allow for movement to the gaps in the helmet meant for seeing, and if you're not mobile enough to easily get up, run and do what anyone in a medieval battlefield must be able to do, any small group can simply knock you over and jab a knife into your eyes through that gap.
Now, how did they partially solve this issue? Well if you seen the video you'll likely see it at 0:40,but if you didn't, here it is:
From these you can easily see how they deal with not leaving the regions near the joints completely unprotected: some armored knights would simply wear a layer of chainmail below the plate armor, covering the chest and limbs so that the region wasn't left completely unprotected. This kind of mixing different armors wasn't uncommon, and it isn't unheard of knights that'd wear variations of the gambeson, a cloth armor, in their chests below the plate for further protection and for helping deal with blows dealt to the armor.
Summing up, just use a proper chainmail below the armor, preferably a ribbited one since it is more durable than ring chainmail. Since chainmail was created before plate armor, I doubt they'd have the tech to make an unobtanium plate armor, but not an unobtanium chainmail.
"but what about guns?" well the main reason plate armor went out of fashion was because better guns started appearing, guns that could penetrate the plate armor without a problem. However, your plate armor is indestructible, and if the properties of unobtanium you mentioned are applicable to processed unobtanium rather than just to the unobtanium processed into armor, then chances are that it is still something one can use practically to protect themselves against firearms, especially if you add in other neat things like bulletproof transparent plastics for the armor visor and other more "modern" things that weren't present.
In regards of how well it'd fare against other weapon and sci-fi elements you'd have to explain better WHAT this armor is mostly meant to protect you from, but if we're talking about melee weapons and even certain firearms, a properly made version of a Gothic plate armor with a layer of proper chainmail underneath will most likely be more than capable of doing its job properly.