First, from Boundless.com (Chemical Composition of Urine), "Urine is an aqueous solution of greater than 95% water, with the remaining constituents, in order of decreasing concentration urea 9.3 g/L, chloride 1.87 g/L, sodium 1.17 g/L, potassium 0.750 g/L, creatinine 0.670 g/L and other dissolved ions, inorganic and organic compounds (proteins, hormones, metabolites)."
Urine color is generally a result of the degradation of the heme molecule from blood into the urinary products, called bilirubin, urobilinogen, urochrome, urobilin and uroerythrin. In essence, they are all tetrapyrroles amounting to something on the order of 1mg per 100ml (or roughly 0.001% of urine)... so this is a very minor part of urine. Also, it should be noted that over 3,000 chemicals have been found in urine, so there's something to consider.
Activated carbon filtration might be able to be used to preferentially remove the tetrapyrroles and some other organic molecules while allowing urea to pass (for the most part).
There are various forms of activated carbon (of course), and so the amount of urea absorption (by carbon) will be variable; the adsorption capacity of the activated carbon for urea will (likely) be different for activated carbon from different sources. Absorbance of urea from one report was about 1.69 mg urea/g carbon, where the urea concentration was 100 mg/L (see picture below). At greater concentrations (like 930mg urea per liter), lesser amounts of acivated carbon will become saturated; in other words the activated carbon will not be able to absorb more urea, but it might be able to effectively remove the tetrapyrroles or some other minor stuff.
But I think that the first thing to do is deal with the concentration. Urea is only about 0.93% of urine. So you only have about 0.93g urea per 100ml of urine.
To concentrate urea: boil off the water (which will also kill bacteria). Urea doesn't boil. The melting point for pure urea is 132.7 °C and urea will begin to decompose at around 150 °C. The residue (which should look creamy) will have a relatively high urea concentration which can then be extracted with (warm/hot 60 °C) ethanol or diacetone alcohol. Salt and protein are significantly less soluble in alcohol(s), so they should hopefully be (mostly) removed at this step.
The solubility of urea in 95% alcohol (100 g/L), absolute ethanol (50 g/L), and methanol (166 g/L) at 20 °C (room temperature) sounds pretty fair. And from TECHNICAL MEMORANDUM No. 13/M/67 (Investigations of Crystal Modification of Urea) "in the case of diacetone alcohol the solubility [of urea] ranged from 2 per cent at 20 °C to about 10 per cent at 100 °C, offering possible development of a process yielding free-flowing crystalline urea."
The solubility of salt (at 25 °C) in ethanol (0.65 g/L) and methanol (14.9 g/L) is significantly lower.
Now, the solubility of a hodgepodge of stuff including tetrapyrroles is something that you will have to experiment with. But, many similar compounds are readily soluble in acetone and tetrachloroethylene (often had as brake cleaner). Urea should not be highly soluble in these two solvents, but I'm a afraid I can't find a reliable solubility listed online, and I happen to be out of acetone right now. Cleaning an alcoholic extract of boiled urine with tetrachloroethylene might require using a separatory funnel.
On a historical note, (around 1727) Herman Boerhaave was able to extract urea from urine by working with the concentated-by-boiling residue (having the consistency of "fresh cream"). After filter pressing the residue, he allowed it to dry for a year... until he obtained a solid mass with an unknown oily substance (on top). He discarded the oil and rinsed the crystals (filtride) with cold water to remove salt, leaving urea. He then recrystallized the urea from hot water. Previously (in 1669), Hennig Brand discovered the philosophers stone (phosphorus) by cooking the bejeezus out of (lots of) urine.
Personally, instead of waiting a year, I would take a chance on extracting urea from the cream. Also, I read today that boiling urine causes irreparable stink-damage to a home; so get a hot plate and an exension cord and boil it outside. Another recipe (as if I had nitric acid to spare), calls for reacting concentrated urea (say 100g in 100ml water) to make urea nitrate. The addition of nitric acid is exothermic and urea nitrate is explosive, so make sure the solution doesn't boil off (ice bath)... and urea nitrate is precipitated in the freezer. Then after you have clean urea nitrate, you can neutralize the acid under alcohol to recover urea. I would reserve this (nitric acid) method for the final work up, using relatively clean urea.
Also, here's a couple of pay-walled articles that might be useful to you if you really want to do this: Solubility of urea in water-alcohol mixtures and Urea in the history of organic chemistry: Isolation from natural sources