Coefficient of determination is close to 1 but the value of RMSE is large. What does it mean?
Compared to $R^2$ $RMSE$ is dependent on the variance of values. Even if $R^2$ is close to 1 but the standard deviation is high the value of $RMSE$ will also be high. 
$$RMSE=\sigma_{y_{true}}\sqrt{1-R^2}$$
where $\sigma$ is a standard deviation

As can be seen from the formula $RMSE$ and $R^2$ have a strict mathematical relationship that shows that $RMSE$ changes according to standard deviation ($\sigma$) and the higher the standard deviation of the true values the higher the value of $RMSE$.

$RMSE$ shows the deviation of the error in units of the values, while $R^2$ shows the share of variance that is explained by the model. You can explain 99% of the variance ($R^2$) but your numbers are in millions of dollars and your error still varies in thousands of dollars ($RMSE$) Whether thousands of dollars is ok for your error or not depends on the case. If you predict profit plus or minus 1000\$ is ok. If you predict revenue then plus or minus 1000\$ could be a difference between a profitable and a non-profitable company.

Proof of the formula:

According to sklearn the formula for $R^2$ is 

$$R^2 = 1 - \frac{\sum_i^n(y_{true} - y_{pred})^2}{\sum_i^n(y_{true} - \overline{y}_{true})^2}$$

RMSE is 
\begin{align}
RMSE &amp;= {\sqrt{\frac1n\sum_i^n(y_{true} - y_{pred})^2}}
\\RMSE^2 &amp;=\frac1n\sum_i^n(y_{true} - y_{pred})^2
\\\frac{RMSE^2}{\frac1n\sum_i^n(y_{true} - \overline{y}_{true})^2} &amp;=\frac{\frac1n\sum_i^n(y_{true} - y_{pred})^2}{\frac1n\sum_i^n(y_{true} - \overline{y}_{true})^2}
\\\frac{RMSE^2}{\frac1n\sum_i^n(y_{true} - \overline{y}_{true})^2} &amp;=\frac{\sum_i^n(y_{true} - y_{pred})^2}{\sum_i^n(y_{true} - \overline{y}_{true})^2}
\\1-\frac{RMSE^2}{\frac1n\sum_i^n(y_{true} - \overline{y}_{true})^2} &amp;=1-\frac{\sum_i^n(y_{true} - y_{pred})^2}{\sum_i^n(y_{true} - \overline{y}_{true})^2}
\\1-\frac{RMSE^2}{\frac1n\sum_i^n(y_{true} - \overline{y}_{true})^2} &amp;=R^2\\1-\frac{RMSE^2}{\sigma_{y_{true}}^2} &amp;=R^2
\\RMSE&amp;=\sigma_{y_{true}}\sqrt{1-R^2}
\end{align}

where $\sigma$ is a standard deviation and $\overline{y}$ is an average