I am not 100% sure with what you are asking for but let me try with the things right off my head.
"附近的" can only be used to mean that somehow physically near by, and it is not used to measure something past in time -- "刚才的" is used to measure the past time.
比 -- to compare.
Example: 你的英语比我好(Your English is better than mine). 比一比，看谁比较重（To compare it, Let use see whom is relatively heavier) Please notice I put a "比较" here.
比较 -- to compare, or relatively, or to some degree.
Example for comparision: 比较下来，我还是最喜欢stackexchange.(After some comparison, I decided that I liked StackExchange best.
Example for relatively: 我比较喜欢吃水果. (I prefer fruits). Please notice the degree of preference here is not that strong, just a slightly inclined intention).
较 -- sometime this is used as a shorten form of 比较. This is not commonly used compared with 比较.
Example: 我比较喜欢两个女人中胸部较大的那个(Among these two women, I prefer the one with bigger boobs). Please note that here again I gave the example of 比较. And if you replace the 较 with 比较, it is 100% ok except a little bit of tendentious.