Okay Walt Kelly said it first. I went into some of the problems of designing a good alien and as I said it's hard. The good ones are all very different but with something that makes us want to relate to them. The mile long aerofauna of a Jovian world might be fascinating creatures but few would want to risk the dangers of descent into their hell world to carry on an exchange with any regularity.
Maybe not. They might be the best mathematicians in the galaxy and able to clear up humanity's vague understandings of FTL navigation but you get the idea. On a more extreme case I have no idea how we'd interact with a super intelligent shade of blue ("Mauve! We require mauve to survive! You will give us your mauve or we will inflict plaid upon you!".) Can you trust that marker? True it is labeled cobalt, but I digress.
An easier technique is to take humans or uplifted animals and give them some new tweak or development that makes them alien in some way. I already went over how telepathy can make nearly anyone a creepy bastard. Besides psi, transhumans might be created through genetic engineering or cybernetics.
Cybernetics receives scant treatment in Classic Traveller and as the Imperium developed it was made clear cyborgs were out there. Local laws regarding cyborgs vary. In some locales they may find themselves property. Cyborgs can incite paranoia especially among law officers. Body pistols are hard enough to detect. Having a person who could carry weapons and other contraband internally could give a libertarian fits.
The guidelines for determining whether a cyborg is property or a person are sort of vague (if anyone could help me out I'd appreciate it.) I believe some planets defined it in terms of body mass or volume (there's no mass in Traveller after all only volume.) If your BMI (Bionic Mass Index) is 51% or more you're property. It kind of explains why all those brains in a jar go rogue. If I preserved my consciousness only to be labeled an AI with organic material I'd be pissed too. Conversely, a human brain takes up about 2.5 %. Is a human body with an AI computer replacing the brain regarded as sentient? If the intent is to curb the amount of replacements to dissuade people from becoming walking instruments of insurrection there might be loopholes like this.
Realistically all these cyborgs with super strength and able to run 60 mph have a problem: their humans parts can't stand the load of such stress. Lift an anvil and your Right Hand Man 5000 Bionic Arm (tm) might pop right out of your shoulder. Jump off a roof and your metal legs will take the fall but your hips will be up in your ribcage.
Another problem might be a power source. To operate with a strength of 15 for any length of time your cyborg might have to run around with a laser rifle power pack on his back. A planet trying to restrict cyborg activity might reserve all the good power cells and capacitors for military government use ("Police captured and arrested the cyborg insurgent when he ran to the end of his power line.")
How will a human react to replacing their body with machinery? That's where the 'alien' quality could come in. They might become addicted to replacing as much of themselves as possible to be as powerful and perfect as transhumanly possible. It's an interesting form of addiction and again one that might justify the BMI enforcement. It gets really kinky when you install positive feedback links. Recharging feels so good ... who needs dating? Of course that leads to the cyborg staying home where he can plug in until the power bill arrives.
Being cyborg can mean setting aside human weaknesses. Recycling gear can eliminate (no pun intended) most of the need for food or drink or other things. Eating is a primary area for socializing with humans. Sure topping off your charge and nutrient tank every week is easier but it could lead to you becoming withdrawn. Having an electrically stimulated sleep cycle would reduce the need to sleep (you still need to dream to defrag your brain) but what to do when you're up and everyone else is awake. Maybe after a while texting will seem more efficient than talking. This is happening with plain vanilla human teenagers right now and they don't even have an internal phone though some are coming close.
Maybe after awhile you stop talking to the meat bags entirely. AIs have far more to teach you.
The line where you turn your back on human and embrace the alien is blurry. What's beyond that line is very dark.