Is there an example of a recursive language which is not context sensitive?
Here's a more formal proof, by the standard trick of diagonalization 
(it must be folklore, but I saw it recently here)

Let $G_1, G_2, ...$ be some enumeration of context sensitive grammars (convince yourself that there are only countable many of them; Why can they be enumerated?),

Let $x_1, x_2, \ldots,$ be enumeration of $\Sigma^*$ (i.e., $x_1=\epsilon$, $x_2=0$, $x_3=1$, $x_4=00$, etc. in the case of binary alphabet).

Consider the language:

$$L = \{ x_i \mid x_i \notin L(G_i)\}.$$

Claim 1 $L$ is not context sensitive: if it was, there was a specific $G_j$ generating it, but $x_j\in L$ while $x_j \notin G_j$.

Claim 2 $L$ is decidable: given $x_i$ we just check if $G_i$ generates it (this problem is known to be PSPACE complete, thus decidable).