The point is an elliptic curve doesn't actually look anything like a curve when evaluated over a finite field, and indeed there's no real way of visualising points in $\mathbb{F}_{29}\times\mathbb{F}_{29}$ that doesn't loose some of the structure anyway.
The best I can think of would be to plot them simple as points in a $29\times29$ grid and join the dots, but even this would be painfully unclear, since for example when would you 'join' them by overflowing the grid (eg: would the line from $(1,5)\to(4,19)$ go straight from one to the other, or would it go out one side and reappear on the opposite side?).
If you were to evaluate $E(\mathbb{R})$ then the resulting points would form a curve in $\mathbb{R}^2$, which you could then plot.