How to optimize my movement & collision code?

Step 1 - Don't check collisions in each key, test them at the end

In your example, you are checking collisions for each key independantly. This will cause some trouble and code replication. In order to avoid that, I would suggest you use temporary variables that will stock the movement, increment it for each key and test collisions only once at the end:

public void MovePlayer()
{
    KeyboardState keyState = Keyboard.GetState(); 

    float xPlus = 0;
    float yPlus = 0;

    if (keyState.IsKeyDown(Keys.Left))
    {
        xPlus -= speed;
    }
    if (keyState.IsKeyDown(Keys.Right))
    {
        xPlus += speed;
    }
    if (keyState.IsKeyDown(Keys.Up))
    {
        yPlus -= speed;
    }
    if (keyState.IsKeyDown(Keys.Down))
    {
        yPlus += speed;
    }

    Rectangle checkRect = new Rectangle((int)(location.X + xPlus), (int)(location.Y + yPlus), texture.Width, texture.Height);
    bool collides = CheckCollision(checkRect);
    if (!collides) {
        location.x += xPlus;
        location.y += yPlus;
    }
}

Step 2 - Independant X and Y movement

A nice thing to add if independant movement for X and Y so that if the player is moving diagonaly, and is hitting a wall on one axis, it will still move on the other axis:

Rectangle checkRect = new Rectangle((int)(location.X + xPlus), (int)location.Y, texture.Width, texture.Height);
bool collides = CheckCollision(checkRect);
if (!collides) {
    location.x += xPlus;
}
checkRect = new Rectangle((int)location.X, (int)(location.Y + yPlus), texture.Width, texture.Height);
collides = CheckCollision(checkRect);
if (!collides) {
    location.y += yPlus;
}

Step 3 - Simplify the CheckCollision method

You have a lot of useless lines in your collision method. It can be simplified as such:

private bool CheckCollision(Rectangle checkRect)
{
    foreach (Tile t in blockedTiles)
    {
        if (t.rectBounds.Intersects(checkRect))
        {
            return true;
        }
    }
    return false;
}

Tip - Always use the true position of your object

You were assigning an intermediary variable that stocked the position of your player. The problem with this is the following: if you move your player, the checkVec variable will not be updated, so the next collision check will most likely fail. Always use the true position of the player, or at least update the checkVec when you move it.

Warning - Don't use += in tests!

When you use += in your ifs, it WILL modify the value! Use only + instead! This is probably the reason why your collisions won't work.

EDIT: Fixed-step vs variable-time

As Shiro pointed out in the comments, this method is not 100% applicable in the case the user modifies the default tiem step method for the variable time step. In this case, we should take into account the time elapsed between two Update(). More details in the link Shiro provided in the comments, and on this site.