Number 88 from the digits 2 0 1 and 7

For that matter, in base 86: 12 + 0*7

If floor were allowed, then this works:

$\left\lfloor\sqrt{10!!}\right\rfloor + 27 $

because

$10!!$ is $10\cdot 8\cdot 6\cdot 4\cdot 2 = 3840 $
$\sqrt{3840} = 61.9677335393\cdots.$

Because modern math is done with computers, here's some Python:

>>> int(str(0 + 1 + 7) * 2)
88

We can do it without the $0$...

$S=\{1,2,7\}$

$(\sum{S}-|S|)\times\prod{S}-\sum{S}$

(using the sum, $\sum$, cardinality, $||$, and product,$\prod$, of the set $S$.)

Evaluated:
$=(10-3)\times 14-10$
$=7\times 14-10$
$=98-10$
$=88$

So, obviously we could just add zero afterwards.

Mind you, I suppose that we could also do it with just one of the numbers in that case too.

$S = \{x\}$

$(|S|+|S|+|S|+|S|+|S|+|S|+|S|+|S|+|S|+|S|+|S|)\times(|S|+|S|)\times(|S|+|S|)\times(|S|+|S|)$
$=(1+1+1+1+1+1+1+1+1+1+1)\times(1+1)\times(1+1)\times(1+1)$
$=11\times2 \times2 \times2$
$=88$

...so
For $x = $...$7$, $2$, or $1$ just multiply the rest together and add them on.
For $x=0$ one can add $(7\times 2)\pmod{1}=0$, or $(7+1)\pmod{2}=0$.

The only question is: Does doing what I have done here count as using the given numbers more than once?

Here is an alternative, sneaky way...

Subtract the one from the seven, turn the resulting six upside-down, append the zero, then subtract the two.

$7-1=6$
$\text{turn}(6)=9$
$\text{append}(9,0)=90$
$90-2=88$

If ceiling or nearest integer function is allowed,

$\lceil{\tan^{-1}(27+0!)}\rceil = 88^{\circ}$

If we use base 36

We now have access to the digits 2, 0, 1, A, N, D, 7. So:
$= (N \times D) - 7 + \left(\frac{A}{2}\right) - 1 + 0$
$= 8B - 7 + 5 - 1 + 0$
$= 8B - 3$
$= 88$
Using base 10 math gives us 2, 0, 1, 10, 13, 23, 7
$= (23 \times 13) - 7 + \left(\frac{10}{2}\right) - 1 + 0$
$= 299 - 7 + 5 - 1 + 0$
$= 299 - 3$
$= 296$
296 is 88 in base 36

As a perl one-liner you could write:

perl -le 'for ($_=-1-2,$i = 0; $i<7; $i++) {$_+= $i*$i }; print'

or without a zero:

perl -le 'print ((7+1)x2)'

or without a zero OR a two in the bash shell:

x=$((7+1)) && echo $x$x

or without a zero, one, or two in bash:

false || x=$((7+$?)) && echo $x$x

or without any numbers at all:

false || x=$(($?+$?+$?+$?+$?+$?+$?+$?)) && echo $x$x

Here is my first answer after about 5 minutes of brute-force checks!

$\lceil\log{\sqrt{102!}}\rceil+7=88$

where log means logarithm in base 10.

By the way, as a wild guess, I think that 88 is very likely to be the OP's birth year.