An effective Twitter-based surveillance system should provide insights at national and subnational levels. The literature identifies two methodologies for geolocating tweets: using only geotagged tweets or retrieving and geolocating all relevant tweets, then filtering out those not belonging to the target geographical region.The first methodology is accurate, cost-effective, and time-efficient but has limited coverage. The second offers better coverage but is less accurate, particularly for informal Arabic text, and is neither cost-effective nor time-efficient due to Twitter's new policies. There is a gap in the literature for an accurate, cost-effective, and time-efficient solution with reasonable coverage at national and subnational levels. To fill this gap, we propose a methodology that uses an underutilized feature in the Twitter backend to geolocate tweets during data collection.This retrieves both geotagged and geolocated tweets, ensuring accuracy and better coverage. It is also cost-effective and time-efficient as only the target tweets are retrieved. Applying this to Saudi Arabia for COVID-19, we generated a dataset, KSAGeoCOV, with 4.25 times more tweets than a geotagged-only dataset. It successfully predicted two COVID-19 outbreaks in June 2021 and January 2022. The Pearson correlation coefficient between WHO weekly reported cases and weekly returned tweets, with a 1-week lag, is r = 0.733; p < 0.001 for Arabic tweets and r = 0.814; p < 0.001 when including English tweets, indicating a very strong correlation at the national level. At the subnational level, top-populated provinces show strong correlations ( r = 0.64 to 0.74; p < 0.003).